Mendelian Randomization Report
Genetic causal association of metabolic syndrome and its components on bladder cancer: A two-sample mendelian randomization
created by Ali Taghavi Rad
2024-09-13
- Abbreviations:
- MetS : metabolic syndrome
- WC : waist circumference
- TG : triglycerides
- HDL : high-density lipoprotein
- DBP : diastolic blood pressure
- Hypertension : Hypertension
- SBP : systolic blood pressure
- FBG : Fasting blood glucose
- BC : bladder cancer
Mendelian Randomization Report [Metabolic Syndrome on bladder cancer]
MetS on BC
Introduction
Title: Investigating the causality between MetS on BC
- Exposure: MetS, GWAS summary statistics: GWAS catalog Database | Reference paper: Lind L, 2019
- Sample size:291,107
- Ancestry: European
- Outcome: BC, GWAS summary statistics: University of Bristol | Reference paper: Burrows K et al., 2017
- Sample size:373,297 , Number of cases:1,279 , Number of controls: 372,016
- Ancestry: European
Data Preparation
1- Number of total SNPs in exposure: 9,463,307 SNPs
2- Number of SNPs exposure with p-value < \(5 \times 10^{-8}\): 7,845 SNPs
3- Number of SNPs exposure after clumping : 85 SNPs
4- Number of total SNPs in outcome: 9,904,926 SNPs
5- Number of common variants between exposure and outcome: 73 SNPs
6- Number of SNPs after harmonization (action=2) = 70 SNPs
(rs3949781, rs5112, rs9971210 being palindromic and were removed)
Checking weakness of the instruments:
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 29.76 36.35 45.11 73.95 75.83 421.53How many SNPs have been eliminated with checking the weakness: 0 SNP
RUN an initial MR:
## id.exposure id.outcome outcome exposure method nsnp
## 1 7jXcAG lz4JOx outcome exposure MR Egger 70
## 2 7jXcAG lz4JOx outcome exposure Weighted median 70
## 3 7jXcAG lz4JOx outcome exposure Inverse variance weighted 70
## 4 7jXcAG lz4JOx outcome exposure Simple mode 70
## 5 7jXcAG lz4JOx outcome exposure Weighted mode 70
## b se pval
## 1 -2.717526e-04 0.0006554467 0.6797349
## 2 3.568013e-04 0.0004299056 0.4065655
## 3 2.480041e-04 0.0002884809 0.3899602
## 4 7.860014e-05 0.0009352226 0.9332646
## 5 4.067502e-06 0.0006829852 0.9952654
## id.exposure id.outcome outcome exposure method Q
## 1 7jXcAG lz4JOx outcome exposure MR Egger 61.42529
## 2 7jXcAG lz4JOx outcome exposure Inverse variance weighted 62.20519
## Q_df Q_pval
## 1 68 0.7003356
## 2 69 0.7058504## id.exposure id.outcome outcome exposure egger_intercept se
## 1 7jXcAG lz4JOx outcome exposure 3.841143e-05 4.349532e-05
## pval
## 1 0.3802849
Testing Outlier with PRESSO test
## $`Main MR results`
## Exposure MR Analysis Causal Estimate Sd T-stat
## 1 beta.exposure Raw 0.0002480041 0.0002739087 0.9054259
## 2 beta.exposure Outlier-corrected NA NA NA
## P-value
## 1 0.3683906
## 2 NA
##
## $`MR-PRESSO results`
## $`MR-PRESSO results`$`Global Test`
## $`MR-PRESSO results`$`Global Test`$RSSobs
## [1] 63.87338
##
## $`MR-PRESSO results`$`Global Test`$Pvalue
## [1] 0.717Radial test
##
## Radial IVW
##
## Estimate Std.Error t value Pr(>|t|)
## Effect (Mod.2nd) 0.0002480038 0.0002739089 0.9054245 0.3652406
## Iterative 0.0002480038 0.0002739089 0.9054245 0.3652406
## Exact (FE) 0.0002516285 0.0002885022 0.8721890 0.3831053
## Exact (RE) 0.0002512773 0.0002633104 0.9543009 0.3432627
##
##
## Residual standard error: 0.949 on 69 degrees of freedom
##
## F-statistic: 0.82 on 1 and 69 DF, p-value: 0.368
## Q-Statistic for heterogeneity: 62.19634 on 69 DF , p-value: 0.7061283
##
## No significant outliers
## Number of iterations = 2## [1] "No significant outliers"Studentized residuals:
Cook’s distance
In statistics, Cook’s distance or Cook’s D is a commonly used estimate of the influence of a data point when performing a least-squares regression analysis.[1] In a practical ordinary least squares analysis, Cook’s distance can be used in several ways:
1- To indicate influential data points that are particularly worth checking for validity.
2- To indicate regions of the design space where it would be good to be able to obtain more data points. It is named after the American statistician R. Dennis Cook, who introduced the concept in 1977(Refernce).
Potential Outliers and Influential SNPs
## 13 14 39 63
## 0.3934785 0.3949920 0.1058180 0.4551633## [1] 13 29 48 63report After Deleting Influential SNPs:
## id.exposure id.outcome outcome exposure method nsnp
## 1 7jXcAG lz4JOx outcome exposure MR Egger 49
## 2 7jXcAG lz4JOx outcome exposure Weighted median 49
## 3 7jXcAG lz4JOx outcome exposure Inverse variance weighted 49
## 4 7jXcAG lz4JOx outcome exposure Simple mode 49
## 5 7jXcAG lz4JOx outcome exposure Weighted mode 49
## b se pval
## 1 0.0008373382 0.0008464392 0.32760756
## 2 0.0006136787 0.0005149885 0.23340410
## 3 0.0007774423 0.0003614456 0.03148214
## 4 0.0009583264 0.0008833201 0.28337880
## 5 0.0006385041 0.0006720742 0.34684606
## id.exposure id.outcome outcome exposure method Q
## 1 7jXcAG lz4JOx outcome exposure MR Egger 19.80711
## 2 7jXcAG lz4JOx outcome exposure Inverse variance weighted 19.81323
## Q_df Q_pval
## 1 47 0.9998349
## 2 48 0.9998953## id.exposure id.outcome outcome exposure egger_intercept se
## 1 7jXcAG lz4JOx outcome exposure -4.203219e-06 5.371135e-05
## pval
## 1 0.9379569
OR report:
## id.exposure id.outcome outcome exposure method nsnp
## 1 7jXcAG lz4JOx outcome exposure MR Egger 49
## 2 7jXcAG lz4JOx outcome exposure Weighted median 49
## 3 7jXcAG lz4JOx outcome exposure Inverse variance weighted 49
## 4 7jXcAG lz4JOx outcome exposure Simple mode 49
## 5 7jXcAG lz4JOx outcome exposure Weighted mode 49
## b se pval lo_ci up_ci or
## 1 0.0008373382 0.0008464392 0.32760756 -0.0008216827 0.002496359 1.000838
## 2 0.0006136787 0.0005149885 0.23340410 -0.0003956987 0.001623056 1.000614
## 3 0.0007774423 0.0003614456 0.03148214 0.0000690089 0.001485876 1.000778
## 4 0.0009583264 0.0008833201 0.28337880 -0.0007729809 0.002689634 1.000959
## 5 0.0006385041 0.0006720742 0.34684606 -0.0006787612 0.001955769 1.000639
## or_lci95 or_uci95
## 1 0.9991787 1.002499
## 2 0.9996044 1.001624
## 3 1.0000690 1.001487
## 4 0.9992273 1.002693
## 5 0.9993215 1.001958MendelianRandomization Package
##
## Inverse-variance weighted method
## (variants uncorrelated, random-effect model)
##
## Number of Variants : 49
##
## ------------------------------------------------------------------
## Method Estimate Std Error 95% CI p-value
## IVW 0.001 0.000 0.000, 0.001 0.031
## ------------------------------------------------------------------
## Residual standard error = 0.642
## Residual standard error is set to 1 in calculation of confidence interval when its estimate is less than 1.
## Heterogeneity test statistic (Cochran's Q) = 19.8132 on 48 degrees of freedom, (p-value = 0.9999). I^2 = 0.0%.
## F statistic = 67.5.## Method Estimate Std Error 95% CI P-value
## Simple median 0.001 0.001 0.000 0.002 0.109
## Weighted median 0.001 0.001 0.000 0.002 0.230
## Penalized weighted median 0.001 0.001 0.000 0.002 0.230
##
## IVW 0.001 0.000 0.000 0.001 0.031
## Penalized IVW 0.001 0.000 0.000 0.001 0.031
## Robust IVW 0.001 0.000 0.000 0.001 0.004
## Penalized robust IVW 0.001 0.000 0.000 0.001 0.004
##
## MR-Egger 0.001 0.001 -0.001 0.002 0.323
## (intercept) 0.000 0.000 0.000 0.000 0.938
## Penalized MR-Egger 0.001 0.001 -0.001 0.002 0.323
## (intercept) 0.000 0.000 0.000 0.000 0.938
## Robust MR-Egger 0.001 0.000 0.000 0.002 0.077
## (intercept) 0.000 0.000 0.000 0.000 0.901
## Penalized robust MR-Egger 0.001 0.000 0.000 0.002 0.077
## (intercept) 0.000 0.000 0.000 0.000 0.901
| id.exposure | id.outcome | exposure | outcome | snp_r2.exposure | snp_r2.outcome | correct_causal_direction | steiger_pval |
|---|---|---|---|---|---|---|---|
| 7jXcAG | lz4JOx | exposure | outcome | 0.0178383 | 6.54e-05 | TRUE | 0 |
## $r2_exp
## [1] 0
##
## $r2_out
## [1] 0.25
##
## $r2_exp_adj
## [1] 0
##
## $r2_out_adj
## [1] 0.25
##
## $correct_causal_direction
## [1] FALSE
##
## $steiger_test
## [1] 0
##
## $correct_causal_direction_adj
## [1] FALSE
##
## $steiger_test_adj
## [1] 0
##
## $vz
## [1] NaN
##
## $vz0
## [1] 0
##
## $vz1
## [1] NaN
##
## $sensitivity_ratio
## [1] NaN
##
## $sensitivity_plot
MRraps package
## $beta.hat
## [1] 0.0007821548
##
## $beta.se
## [1] 0.0003688363
##
## $beta.p.value
## [1] 0.03395538
##
## $naive.se
## [1] 0.0003660649
##
## $chi.sq.test
## [1] 19.78523## over.dispersion loss.function beta.hat beta.se
## 1 FALSE l2 0.0007821548 0.0003688363
## 2 FALSE huber 0.0007821534 0.0003784179
## 3 FALSE tukey 0.0007765945 0.0003784110
## 4 TRUE l2 0.0007950524 0.0004204950
## 5 TRUE huber 0.0007824554 0.0003784268
## 6 TRUE tukey 0.0007798699 0.0003784242##
## MR-Lasso method
##
## Number of variants : 49
## Number of valid instruments : 49
## Tuning parameter : 0.1785468
## ------------------------------------------------------------------
## Exposure Estimate Std Error 95% CI p-value
## exposure 0.001 0.000 0.000, 0.001 0.031
## ------------------------------------------------------------------##
## Constrained maximum likelihood method (MRcML)
## Number of Variants: 49
## Results for: cML-MA-BIC
## ------------------------------------------------------------------
## Method Estimate SE Pvalue 95% CI
## cML-MA-BIC 0.001 0.000 0.031 [0.000,0.001]
## ------------------------------------------------------------------##
## Debiased inverse-variance weighted method
## (Over.dispersion:TRUE)
##
## Number of Variants : 49
## ------------------------------------------------------------------
## Method Estimate Std Error 95% CI p-value Condition
## dIVW 0.001 0.000 0.000, 0.002 0.032 465.263
## ------------------------------------------------------------------##
## Mode-based method of Hartwig et al
## (weighted, delta standard errors [not assuming NOME], bandwidth factor = 1)
##
## Number of Variants : 49
## ------------------------------------------------------------------
## Method Estimate Std Error 95% CI p-value
## MBE 0.001 0.001 -0.001, 0.002 0.349
## ------------------------------------------------------------------
WC on BC
Introduction
Title: Investigating the causality between WC on BC
- Exposure: WC, GWAS summary statistics: OpenGWAS | Reference paper: Elsworth B et al., 2018
- Sample size: 462,166
- Ancestry: European
- Outcome: BC, GWAS summary statistics: University of Bristol | Reference paper: Burrows K et al., 2017
- Sample size:373,297 , Number of cases:1,279 , Number of controls: 372,016
- Ancestry: European
Data Preparation
1- Number of total SNPs in exposure: 9,463,307 SNPs
2- Number of SNPs exposure with p-value < \(5 \times 10^{-8}\): 40,966 SNPs
3- Number of SNPs exposure after clumping : 375 SNPs
4- Number of total SNPs in outcome: 9,904,926 SNPs
5- Number of common variants between exposure and outcome: 338 SNPs
6- Number of SNPs after harmonization (action=2) = 325 SNPs
(rs10406327, rs10887578, rs11666480, rs11778934, rs1405261, rs1441098, rs1454687, rs165656, rs2373980, rs347551, rs3949781, rs4856717, rs654060 being palindromic and were removed)
Checking weakness of the instruments:
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 29.70 34.92 42.79 57.70 59.44 940.08How many SNPs have been eliminated with checking the weakness: 0 SNP
RUN an initial MR:
## id.exposure id.outcome outcome exposure method nsnp
## 1 gQWuOt hk2Grt outcome exposure MR Egger 325
## 2 gQWuOt hk2Grt outcome exposure Weighted median 325
## 3 gQWuOt hk2Grt outcome exposure Inverse variance weighted 325
## 4 gQWuOt hk2Grt outcome exposure Simple mode 325
## 5 gQWuOt hk2Grt outcome exposure Weighted mode 325
## b se pval
## 1 0.0004851254 0.0015935854 0.76100102
## 2 0.0019680361 0.0009068006 0.02998355
## 3 0.0007836522 0.0005521999 0.15585649
## 4 0.0038565942 0.0027013483 0.15435420
## 5 0.0027540038 0.0020488110 0.17982540
## id.exposure id.outcome outcome exposure method Q
## 1 gQWuOt hk2Grt outcome exposure MR Egger 310.8984
## 2 gQWuOt hk2Grt outcome exposure Inverse variance weighted 310.9383
## Q_df Q_pval
## 1 323 0.675767
## 2 324 0.689309## id.exposure id.outcome outcome exposure egger_intercept se
## 1 gQWuOt hk2Grt outcome exposure 4.911427e-06 2.459367e-05
## pval
## 1 0.8418386
Testing Outlier with PRESSO test
## $`Main MR results`
## Exposure MR Analysis Causal Estimate Sd T-stat
## 1 beta.exposure Raw 0.0007836522 0.0005409547 1.448647
## 2 beta.exposure Outlier-corrected NA NA NA
## P-value
## 1 0.1484034
## 2 NA
##
## $`MR-PRESSO results`
## $`MR-PRESSO results`$`Global Test`
## $`MR-PRESSO results`$`Global Test`$RSSobs
## [1] 312.9557
##
## $`MR-PRESSO results`$`Global Test`$Pvalue
## [1] 0.673Radial test
##
## Radial IVW
##
## Estimate Std.Error t value Pr(>|t|)
## Effect (Mod.2nd) 0.0007836521 0.0005409547 1.448646 0.1474363
## Iterative 0.0007836521 0.0005409547 1.448646 0.1474363
## Exact (FE) 0.0007969929 0.0005522305 1.443225 0.1489571
## Exact (RE) 0.0007971043 0.0005467433 1.457913 0.1458331
##
##
## Residual standard error: 0.98 on 324 degrees of freedom
##
## F-statistic: 2.1 on 1 and 324 DF, p-value: 0.148
## Q-Statistic for heterogeneity: 310.9049 on 324 DF , p-value: 0.689785
##
## No significant outliers
## Number of iterations = 2## [1] "No significant outliers"Studentized residuals:
Cook’s distance
In statistics, Cook’s distance or Cook’s D is a commonly used estimate of the influence of a data point when performing a least-squares regression analysis.[1] In a practical ordinary least squares analysis, Cook’s distance can be used in several ways:
1- To indicate influential data points that are particularly worth checking for validity.
2- To indicate regions of the design space where it would be good to be able to obtain more data points. It is named after the American statistician R. Dennis Cook, who introduced the concept in 1977(Refernce).
Potential Outliers and Influential SNPs
## 44 69 87 97 157 161 184
## 0.02126731 0.22101306 0.01745966 0.31847637 0.01750254 0.02205178 0.22280641
## 193 202 209 215 216 232 274
## 0.09906164 0.02447554 0.03537849 0.02763198 0.03682358 0.01686872 0.02093784
## 285 312
## 0.02300973 0.02724397## [1] 42 69 72 77 97 102 161 165 184 193 202 211 216 223 232 236 292 312report After Deleting Influential SNPs:
## id.exposure id.outcome outcome exposure method nsnp
## 1 gQWuOt hk2Grt outcome exposure MR Egger 300
## 2 gQWuOt hk2Grt outcome exposure Weighted median 300
## 3 gQWuOt hk2Grt outcome exposure Inverse variance weighted 300
## 4 gQWuOt hk2Grt outcome exposure Simple mode 300
## 5 gQWuOt hk2Grt outcome exposure Weighted mode 300
## b se pval
## 1 0.001438162 0.0023135435 0.53466208
## 2 0.002016313 0.0008781334 0.02166818
## 3 0.001584878 0.0006181852 0.01035455
## 4 0.003779784 0.0028239192 0.18175405
## 5 0.003004811 0.0025216609 0.23436307
## id.exposure id.outcome outcome exposure method Q
## 1 gQWuOt hk2Grt outcome exposure MR Egger 217.4532
## 2 gQWuOt hk2Grt outcome exposure Inverse variance weighted 217.4576
## Q_df Q_pval
## 1 298 0.9998564
## 2 299 0.9998785## id.exposure id.outcome outcome exposure egger_intercept se
## 1 gQWuOt hk2Grt outcome exposure 2.176654e-06 3.307549e-05
## pval
## 1 0.9475743
OR report:
## id.exposure id.outcome outcome exposure method nsnp
## 1 gQWuOt hk2Grt outcome exposure MR Egger 300
## 2 gQWuOt hk2Grt outcome exposure Weighted median 300
## 3 gQWuOt hk2Grt outcome exposure Inverse variance weighted 300
## 4 gQWuOt hk2Grt outcome exposure Simple mode 300
## 5 gQWuOt hk2Grt outcome exposure Weighted mode 300
## b se pval lo_ci up_ci or
## 1 0.001438162 0.0023135435 0.53466208 -0.0030963829 0.005972707 1.001439
## 2 0.002016313 0.0008781334 0.02166818 0.0002951711 0.003737454 1.002018
## 3 0.001584878 0.0006181852 0.01035455 0.0003732347 0.002796521 1.001586
## 4 0.003779784 0.0028239192 0.18175405 -0.0017550976 0.009314666 1.003787
## 5 0.003004811 0.0025216609 0.23436307 -0.0019376441 0.007947267 1.003009
## or_lci95 or_uci95
## 1 0.9969084 1.005991
## 2 1.0002952 1.003744
## 3 1.0003733 1.002800
## 4 0.9982464 1.009358
## 5 0.9980642 1.007979MendelianRandomization Package
##
## Inverse-variance weighted method
## (variants uncorrelated, random-effect model)
##
## Number of Variants : 300
##
## ------------------------------------------------------------------
## Method Estimate Std Error 95% CI p-value
## IVW 0.002 0.001 0.000, 0.003 0.010
## ------------------------------------------------------------------
## Residual standard error = 0.853
## Residual standard error is set to 1 in calculation of confidence interval when its estimate is less than 1.
## Heterogeneity test statistic (Cochran's Q) = 217.4576 on 299 degrees of freedom, (p-value = 0.9999). I^2 = 0.0%.
## F statistic = 49.9.## Method Estimate Std Error 95% CI P-value
## Simple median 0.002 0.001 0.001 0.004 0.005
## Weighted median 0.002 0.001 0.000 0.004 0.021
## Penalized weighted median 0.002 0.001 0.000 0.004 0.019
##
## IVW 0.002 0.001 0.000 0.003 0.010
## Penalized IVW 0.002 0.001 0.000 0.003 0.010
## Robust IVW 0.002 0.001 0.000 0.003 0.008
## Penalized robust IVW 0.002 0.001 0.000 0.003 0.008
##
## MR-Egger 0.001 0.002 -0.003 0.006 0.534
## (intercept) 0.000 0.000 0.000 0.000 0.948
## Penalized MR-Egger 0.001 0.002 -0.003 0.006 0.534
## (intercept) 0.000 0.000 0.000 0.000 0.948
## Robust MR-Egger 0.001 0.002 -0.003 0.005 0.623
## (intercept) 0.000 0.000 0.000 0.000 0.775
## Penalized robust MR-Egger 0.001 0.002 -0.003 0.005 0.623
## (intercept) 0.000 0.000 0.000 0.000 0.775
| id.exposure | id.outcome | exposure | outcome | snp_r2.exposure | snp_r2.outcome | correct_causal_direction | steiger_pval |
|---|---|---|---|---|---|---|---|
| gQWuOt | hk2Grt | exposure | outcome | 0.0323754 | 0.0006007 | TRUE | 0 |
## $r2_exp
## [1] 0
##
## $r2_out
## [1] 0.25
##
## $r2_exp_adj
## [1] 0
##
## $r2_out_adj
## [1] 0.25
##
## $correct_causal_direction
## [1] FALSE
##
## $steiger_test
## [1] 0
##
## $correct_causal_direction_adj
## [1] FALSE
##
## $steiger_test_adj
## [1] 0
##
## $vz
## [1] NaN
##
## $vz0
## [1] 0
##
## $vz1
## [1] NaN
##
## $sensitivity_ratio
## [1] NaN
##
## $sensitivity_plot
MRraps package
## $beta.hat
## [1] 0.001608248
##
## $beta.se
## [1] 0.0006327895
##
## $beta.p.value
## [1] 0.01103711
##
## $naive.se
## [1] 0.0006263816
##
## $chi.sq.test
## [1] 217.3606## over.dispersion loss.function beta.hat beta.se
## 1 FALSE l2 0.001608248 0.0006327895
## 2 FALSE huber 0.001623035 0.0006492334
## 3 FALSE tukey 0.001659829 0.0006492483
## 4 TRUE l2 0.001621952 0.0007175196
## 5 TRUE huber 0.001623411 0.0006492399
## 6 TRUE tukey 0.001660072 0.0006492553##
## MR-Lasso method
##
## Number of variants : 300
## Number of valid instruments : 300
## Tuning parameter : 0.1435915
## ------------------------------------------------------------------
## Exposure Estimate Std Error 95% CI p-value
## exposure 0.002 0.001 0.000, 0.003 0.010
## ------------------------------------------------------------------##
## Constrained maximum likelihood method (MRcML)
## Number of Variants: 300
## Results for: cML-MA-BIC
## ------------------------------------------------------------------
## Method Estimate SE Pvalue 95% CI
## cML-MA-BIC 0.002 0.001 0.010 [0.000,0.003]
## ------------------------------------------------------------------##
## Debiased inverse-variance weighted method
## (Over.dispersion:TRUE)
##
## Number of Variants : 300
## ------------------------------------------------------------------
## Method Estimate Std Error 95% CI p-value Condition
## dIVW 0.002 0.001 0.000, 0.003 0.010 846.644
## ------------------------------------------------------------------##
## Mode-based method of Hartwig et al
## (weighted, delta standard errors [not assuming NOME], bandwidth factor = 1)
##
## Number of Variants : 300
## ------------------------------------------------------------------
## Method Estimate Std Error 95% CI p-value
## MBE 0.003 0.002 -0.001, 0.007 0.182
## ------------------------------------------------------------------
TG on BC
Introduction
Title: Investigating the causality between TG on BC
- Exposure: TG, GWAS summary statistics: GLG Consortium | Reference paper: Willer CJ et al., 2013
- Sample size: 188,577
- Ancestry: European
- Outcome: BC, GWAS summary statistics: University of Bristol | Reference paper: Burrows K et al., 2017
- Sample size:373,297 , Number of cases:1,279 , Number of controls: 372,016
- Ancestry: European
Data Preparation
1- Number of total SNPs in exposure: 2,439,432 SNPs
2- Number of SNPs exposure with p-value < \(5 \times 10^{-8}\): 3,242 SNPs
3- Number of SNPs exposure after clumping : 55 SNPs
4- Number of total SNPs in outcome: 9,904,926 SNPs
5- Number of common variants between exposure and outcome: 49 SNPs
6- Number of SNPs after harmonization (action=2) = 49 SNPs
Checking weakness of the instruments:
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 29.86 39.75 54.34 161.67 139.80 1140.06How many SNPs have been eliminated with checking the weakness: 0 SNP
RUN an initial MR:
## id.exposure id.outcome outcome exposure method nsnp
## 1 tMn5wl 7jXcAG outcome exposure MR Egger 49
## 2 tMn5wl 7jXcAG outcome exposure Weighted median 49
## 3 tMn5wl 7jXcAG outcome exposure Inverse variance weighted 49
## 4 tMn5wl 7jXcAG outcome exposure Simple mode 49
## 5 tMn5wl 7jXcAG outcome exposure Weighted mode 49
## b se pval
## 1 -0.0016251822 0.0007995444 0.0477606
## 2 -0.0010058346 0.0006603498 0.1277126
## 3 -0.0004007591 0.0004863338 0.4099162
## 4 -0.0007659475 0.0011520755 0.5093337
## 5 -0.0010199074 0.0006581437 0.1277890
## id.exposure id.outcome outcome exposure method Q
## 1 tMn5wl 7jXcAG outcome exposure MR Egger 51.56956
## 2 tMn5wl 7jXcAG outcome exposure Inverse variance weighted 55.53372
## Q_df Q_pval
## 1 47 0.2997419
## 2 48 0.2120682## id.exposure id.outcome outcome exposure egger_intercept se
## 1 tMn5wl 7jXcAG outcome exposure 7.299405e-05 3.840251e-05
## pval
## 1 0.06347554
Testing Outlier with PRESSO test
## $`Main MR results`
## Exposure MR Analysis Causal Estimate Sd T-stat
## 1 beta.exposure Raw -0.0004007591 0.0004863338 -0.8240411
## 2 beta.exposure Outlier-corrected NA NA NA
## P-value
## 1 0.4139921
## 2 NA
##
## $`MR-PRESSO results`
## $`MR-PRESSO results`$`Global Test`
## $`MR-PRESSO results`$`Global Test`$RSSobs
## [1] 57.3746
##
## $`MR-PRESSO results`$`Global Test`$Pvalue
## [1] 0.221Radial test
##
## Radial IVW
##
## Estimate Std.Error t value Pr(>|t|)
## Effect (Mod.2nd) -0.0004007595 0.0004863343 -0.8240412 0.4099162
## Iterative -0.0004007595 0.0004863343 -0.8240412 0.4099162
## Exact (FE) -0.0004078146 0.0004521674 -0.9019107 0.3671043
## Exact (RE) -0.0004034230 0.0004359303 -0.9254299 0.3593719
##
##
## Residual standard error: 1.076 on 48 degrees of freedom
##
## F-statistic: 0.68 on 1 and 48 DF, p-value: 0.414
## Q-Statistic for heterogeneity: 55.52826 on 48 DF , p-value: 0.2122145
##
## No significant outliers
## Number of iterations = 2## [1] "No significant outliers"Studentized residuals:
Cook’s distance
In statistics, Cook’s distance or Cook’s D is a commonly used estimate of the influence of a data point when performing a least-squares regression analysis.[1] In a practical ordinary least squares analysis, Cook’s distance can be used in several ways:
1- To indicate influential data points that are particularly worth checking for validity.
2- To indicate regions of the design space where it would be good to be able to obtain more data points. It is named after the American statistician R. Dennis Cook, who introduced the concept in 1977(Refernce).
Potential Outliers and Influential SNPs
## 6 10
## 0.1119431 0.6940430## [1] 11 26 33report After Deleting Influential SNPs:
## id.exposure id.outcome outcome exposure method nsnp
## 1 tMn5wl 7jXcAG outcome exposure MR Egger 31
## 2 tMn5wl 7jXcAG outcome exposure Weighted median 31
## 3 tMn5wl 7jXcAG outcome exposure Inverse variance weighted 31
## 4 tMn5wl 7jXcAG outcome exposure Simple mode 31
## 5 tMn5wl 7jXcAG outcome exposure Weighted mode 31
## b se pval
## 1 -0.0009272501 0.0012178857 0.45258902
## 2 -0.0010867780 0.0008836880 0.21876414
## 3 -0.0013029307 0.0006466567 0.04391803
## 4 -0.0009568986 0.0014385320 0.51101024
## 5 -0.0009967204 0.0008965354 0.27507739
## id.exposure id.outcome outcome exposure method Q
## 1 tMn5wl 7jXcAG outcome exposure MR Egger 10.70223
## 2 tMn5wl 7jXcAG outcome exposure Inverse variance weighted 10.83474
## Q_df Q_pval
## 1 29 0.9992216
## 2 30 0.9994857## id.exposure id.outcome outcome exposure egger_intercept se
## 1 tMn5wl 7jXcAG outcome exposure -1.893036e-05 5.200337e-05
## pval
## 1 0.7184824
OR report:
## id.exposure id.outcome outcome exposure method nsnp
## 1 tMn5wl 7jXcAG outcome exposure MR Egger 31
## 2 tMn5wl 7jXcAG outcome exposure Weighted median 31
## 3 tMn5wl 7jXcAG outcome exposure Inverse variance weighted 31
## 4 tMn5wl 7jXcAG outcome exposure Simple mode 31
## 5 tMn5wl 7jXcAG outcome exposure Weighted mode 31
## b se pval lo_ci up_ci or
## 1 -0.0009272501 0.0012178857 0.45258902 -0.003314306 1.459806e-03 0.9990732
## 2 -0.0010867780 0.0008836880 0.21876414 -0.002818806 6.452504e-04 0.9989138
## 3 -0.0013029307 0.0006466567 0.04391803 -0.002570378 -3.548352e-05 0.9986979
## 4 -0.0009568986 0.0014385320 0.51101024 -0.003776421 1.862624e-03 0.9990436
## 5 -0.0009967204 0.0008965354 0.27507739 -0.002753930 7.604889e-04 0.9990038
## or_lci95 or_uci95
## 1 0.9966912 1.0014609
## 2 0.9971852 1.0006455
## 3 0.9974329 0.9999645
## 4 0.9962307 1.0018644
## 5 0.9972499 1.0007608MendelianRandomization Package
##
## Inverse-variance weighted method
## (variants uncorrelated, random-effect model)
##
## Number of Variants : 31
##
## ------------------------------------------------------------------
## Method Estimate Std Error 95% CI p-value
## IVW -0.001 0.001 -0.003, 0.000 0.044
## ------------------------------------------------------------------
## Residual standard error = 0.601
## Residual standard error is set to 1 in calculation of confidence interval when its estimate is less than 1.
## Heterogeneity test statistic (Cochran's Q) = 10.8347 on 30 degrees of freedom, (p-value = 0.9995). I^2 = 0.0%.
## F statistic = 124.1.## Method Estimate Std Error 95% CI P-value
## Simple median -0.001 0.001 -0.003 0.001 0.162
## Weighted median -0.001 0.001 -0.003 0.001 0.243
## Penalized weighted median -0.001 0.001 -0.003 0.001 0.243
##
## IVW -0.001 0.001 -0.003 0.000 0.044
## Penalized IVW -0.001 0.001 -0.003 0.000 0.044
## Robust IVW -0.001 0.000 -0.002 0.000 0.022
## Penalized robust IVW -0.001 0.000 -0.002 0.000 0.022
##
## MR-Egger -0.001 0.001 -0.003 0.001 0.446
## (intercept) 0.000 0.000 0.000 0.000 0.716
## Penalized MR-Egger -0.001 0.001 -0.003 0.001 0.446
## (intercept) 0.000 0.000 0.000 0.000 0.716
## Robust MR-Egger -0.001 0.001 -0.003 0.000 0.172
## (intercept) 0.000 0.000 0.000 0.000 0.930
## Penalized robust MR-Egger -0.001 0.001 -0.003 0.000 0.172
## (intercept) 0.000 0.000 0.000 0.000 0.930
| id.exposure | id.outcome | exposure | outcome | snp_r2.exposure | snp_r2.outcome | correct_causal_direction | steiger_pval |
|---|---|---|---|---|---|---|---|
| tMn5wl | 7jXcAG | exposure | outcome | 0.0180328 | 4e-05 | TRUE | 0 |
## $r2_exp
## [1] 0
##
## $r2_out
## [1] 0.25
##
## $r2_exp_adj
## [1] 0
##
## $r2_out_adj
## [1] 0.25
##
## $correct_causal_direction
## [1] FALSE
##
## $steiger_test
## [1] 0
##
## $correct_causal_direction_adj
## [1] FALSE
##
## $steiger_test_adj
## [1] 0
##
## $vz
## [1] NaN
##
## $vz0
## [1] 0
##
## $vz1
## [1] NaN
##
## $sensitivity_ratio
## [1] NaN
##
## $sensitivity_plot
MRraps package
## $beta.hat
## [1] -0.001306734
##
## $beta.se
## [1] 0.0006543805
##
## $beta.p.value
## [1] 0.04583574
##
## $naive.se
## [1] 0.0006515952
##
## $chi.sq.test
## [1] 10.82295## over.dispersion loss.function beta.hat beta.se
## 1 FALSE l2 -0.001306734 0.0006543805
## 2 FALSE huber -0.001306734 0.0006713799
## 3 FALSE tukey -0.001264176 0.0006713349
## 4 TRUE l2 -0.001337558 0.0007611713
## 5 TRUE huber -0.001304389 0.0006713843
## 6 TRUE tukey -0.001271652 0.0006713497##
## MR-Lasso method
##
## Number of variants : 31
## Number of valid instruments : 31
## Tuning parameter : 0.2424016
## ------------------------------------------------------------------
## Exposure Estimate Std Error 95% CI p-value
## exposure -0.001 0.001 -0.003, 0.000 0.044
## ------------------------------------------------------------------##
## Constrained maximum likelihood method (MRcML)
## Number of Variants: 31
## Results for: cML-MA-BIC
## ------------------------------------------------------------------
## Method Estimate SE Pvalue 95% CI
## cML-MA-BIC -0.001 0.001 0.044 [-0.003,0.000]
## ------------------------------------------------------------------##
## Debiased inverse-variance weighted method
## (Over.dispersion:TRUE)
##
## Number of Variants : 31
## ------------------------------------------------------------------
## Method Estimate Std Error 95% CI p-value Condition
## dIVW -0.001 0.001 -0.003, 0.000 0.044 685.513
## ------------------------------------------------------------------##
## Mode-based method of Hartwig et al
## (weighted, delta standard errors [not assuming NOME], bandwidth factor = 1)
##
## Number of Variants : 31
## ------------------------------------------------------------------
## Method Estimate Std Error 95% CI p-value
## MBE -0.001 0.001 -0.003, 0.001 0.317
## ------------------------------------------------------------------
HDL on BC
Introduction
Title: Investigating the causality between HDL on BC
- Exposure: HDL, GWAS summary statistics: GLG Consortium | Reference paper: Willer CJ et al., 2013
- Sample size: 187,167
- Ancestry: European
- Outcome: BC, GWAS summary statistics: University of Bristol | Reference paper: Burrows K et al., 2017
- Sample size:373,297 , Number of cases:1,279 , Number of controls: 372,016
- Ancestry: European
Data Preparation
1- Number of total SNPs in exposure: 120,671 SNPs
2- Number of SNPs exposure with p-value < \(5 \times 10^{-8}\): 1,628 SNPs
3- Number of SNPs exposure after clumping : 42 SNPs
4- Number of total SNPs in outcome: 9,904,926 SNPs
5- Number of common variants between exposure and outcome: 40 SNPs
6- Number of SNPs after harmonization (action=2) = 40 SNPs
Checking weakness of the instruments:
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 34.42 42.06 57.36 135.73 120.65 1817.10How many SNPs have been eliminated with checking the weakness: 0 SNP
RUN an initial MR:
## id.exposure id.outcome outcome exposure method nsnp
## 1 JI02GY hk2Grt outcome exposure MR Egger 40
## 2 JI02GY hk2Grt outcome exposure Weighted median 40
## 3 JI02GY hk2Grt outcome exposure Inverse variance weighted 40
## 4 JI02GY hk2Grt outcome exposure Simple mode 40
## 5 JI02GY hk2Grt outcome exposure Weighted mode 40
## b se pval
## 1 -0.0003130527 0.0008773012 0.7231886
## 2 -0.0005919845 0.0005767193 0.3046706
## 3 0.0002086744 0.0004843317 0.6665774
## 4 0.0007916117 0.0012495937 0.5301081
## 5 -0.0007112743 0.0005322064 0.1891432
## id.exposure id.outcome outcome exposure method Q
## 1 JI02GY hk2Grt outcome exposure MR Egger 60.39705
## 2 JI02GY hk2Grt outcome exposure Inverse variance weighted 61.21010
## Q_df Q_pval
## 1 38 0.01185218
## 2 39 0.01305900## id.exposure id.outcome outcome exposure egger_intercept se
## 1 JI02GY hk2Grt outcome exposure 4.214987e-05 5.893206e-05
## pval
## 1 0.4788397
Testing Outlier with PRESSO test
## $`Main MR results`
## Exposure MR Analysis Causal Estimate Sd T-stat
## 1 beta.exposure Raw 2.086744e-04 0.0004843317 0.4308501
## 2 beta.exposure Outlier-corrected 9.034355e-05 0.0004430422 0.2039163
## P-value
## 1 0.6689494
## 2 0.8395070
##
## $`MR-PRESSO results`
## $`MR-PRESSO results`$`Global Test`
## $`MR-PRESSO results`$`Global Test`$RSSobs
## [1] 67.98238
##
## $`MR-PRESSO results`$`Global Test`$Pvalue
## [1] 0.013
##
##
## $`MR-PRESSO results`$`Outlier Test`
## RSSobs Pvalue
## 1 3.673356e-09 1
## 2 2.808632e-08 1
## 3 7.851406e-10 1
## 4 1.223175e-07 0.4
## 5 2.731639e-09 1
## 6 1.217620e-07 1
## 7 5.484050e-09 1
## 8 5.327204e-08 1
## 9 1.397143e-07 0.48
## 10 1.361036e-08 1
## 11 2.095919e-08 1
## 12 3.562765e-10 1
## 13 2.118310e-08 1
## 14 1.230648e-08 1
## 15 4.935965e-08 1
## 16 3.174821e-09 1
## 17 1.956409e-09 1
## 18 8.526203e-08 1
## 19 1.704063e-08 1
## 20 1.444154e-08 1
## 21 6.701960e-12 1
## 22 7.941793e-09 1
## 23 4.373821e-08 1
## 24 8.307344e-08 1
## 25 1.418331e-07 0.8
## 26 7.822265e-08 1
## 27 8.872155e-09 1
## 28 1.308734e-10 1
## 29 1.137428e-10 1
## 30 2.796098e-08 1
## 31 3.056937e-08 1
## 32 3.743604e-13 1
## 33 7.461141e-09 1
## 34 2.076311e-07 0.12
## 35 1.712467e-08 1
## 36 4.623446e-08 1
## 37 1.024587e-08 1
## 38 4.652940e-08 1
## 39 5.177744e-07 <0.04
## 40 1.224732e-11 1
##
## $`MR-PRESSO results`$`Distortion Test`
## $`MR-PRESSO results`$`Distortion Test`$`Outliers Indices`
## [1] 39
##
## $`MR-PRESSO results`$`Distortion Test`$`Distortion Coefficient`
## beta.exposure
## 130.9787
##
## $`MR-PRESSO results`$`Distortion Test`$Pvalue
## [1] 0.384Radial test
##
## Radial IVW
##
## Estimate Std.Error t value Pr(>|t|)
## Effect (Mod.2nd) 0.0002086733 0.0004843315 0.4308481 0.6665788
## Iterative 0.0002086733 0.0004843315 0.4308481 0.6665788
## Exact (FE) 0.0002091666 0.0003866121 0.5410246 0.5884906
## Exact (RE) 0.0002103403 0.0006001667 0.3504697 0.7278722
##
##
## Residual standard error: 1.253 on 39 degrees of freedom
##
## F-statistic: 0.19 on 1 and 39 DF, p-value: 0.669
## Q-Statistic for heterogeneity: 61.20676 on 39 DF , p-value: 0.01306847
##
## Outliers detected
## Number of iterations = 2## SNP Q_statistic p.value
## 1 rs8044791 11.60761 0.0006568235Studentized residuals:
Cook’s distance
In statistics, Cook’s distance or Cook’s D is a commonly used estimate of the influence of a data point when performing a least-squares regression analysis.[1] In a practical ordinary least squares analysis, Cook’s distance can be used in several ways:
1- To indicate influential data points that are particularly worth checking for validity.
2- To indicate regions of the design space where it would be good to be able to obtain more data points. It is named after the American statistician R. Dennis Cook, who introduced the concept in 1977(Refernce).
Potential Outliers and Influential SNPs
## 34
## 1.373054## [1] 34 39report After Deleting Influential SNPs:
## id.exposure id.outcome outcome exposure method nsnp
## 1 JI02GY hk2Grt outcome exposure MR Egger 28
## 2 JI02GY hk2Grt outcome exposure Weighted median 28
## 3 JI02GY hk2Grt outcome exposure Inverse variance weighted 28
## 4 JI02GY hk2Grt outcome exposure Simple mode 28
## 5 JI02GY hk2Grt outcome exposure Weighted mode 28
## b se pval
## 1 0.001444222 0.0016993868 0.40316735
## 2 0.001223993 0.0008339964 0.14220650
## 3 0.001495770 0.0006210339 0.01601752
## 4 0.001005600 0.0015260057 0.51549289
## 5 0.001005600 0.0014169252 0.48397127
## id.exposure id.outcome outcome exposure method Q
## 1 JI02GY hk2Grt outcome exposure MR Egger 8.744656
## 2 JI02GY hk2Grt outcome exposure Inverse variance weighted 8.745718
## Q_df Q_pval
## 1 26 0.9993785
## 2 27 0.9996541## id.exposure id.outcome outcome exposure egger_intercept se
## 1 JI02GY hk2Grt outcome exposure 2.796185e-06 8.580547e-05
## pval
## 1 0.9742524
OR report:
## id.exposure id.outcome outcome exposure method nsnp
## 1 JI02GY hk2Grt outcome exposure MR Egger 28
## 2 JI02GY hk2Grt outcome exposure Weighted median 28
## 3 JI02GY hk2Grt outcome exposure Inverse variance weighted 28
## 4 JI02GY hk2Grt outcome exposure Simple mode 28
## 5 JI02GY hk2Grt outcome exposure Weighted mode 28
## b se pval lo_ci up_ci or
## 1 0.001444222 0.0016993868 0.40316735 -0.0018865764 0.004775020 1.001445
## 2 0.001223993 0.0008339964 0.14220650 -0.0004106401 0.002858626 1.001225
## 3 0.001495770 0.0006210339 0.01601752 0.0002785437 0.002712996 1.001497
## 4 0.001005600 0.0015260057 0.51549289 -0.0019853714 0.003996571 1.001006
## 5 0.001005600 0.0014169252 0.48397127 -0.0017715737 0.003782773 1.001006
## or_lci95 or_uci95
## 1 0.9981152 1.004786
## 2 0.9995894 1.002863
## 3 1.0002786 1.002717
## 4 0.9980166 1.004005
## 5 0.9982300 1.003790MendelianRandomization Package
##
## Inverse-variance weighted method
## (variants uncorrelated, random-effect model)
##
## Number of Variants : 28
##
## ------------------------------------------------------------------
## Method Estimate Std Error 95% CI p-value
## IVW 0.001 0.001 0.000, 0.003 0.016
## ------------------------------------------------------------------
## Residual standard error = 0.569
## Residual standard error is set to 1 in calculation of confidence interval when its estimate is less than 1.
## Heterogeneity test statistic (Cochran's Q) = 8.7457 on 27 degrees of freedom, (p-value = 0.9997). I^2 = 0.0%.
## F statistic = 73.8.## Method Estimate Std Error 95% CI P-value
## Simple median 0.001 0.001 0.000 0.003 0.116
## Weighted median 0.001 0.001 0.000 0.003 0.135
## Penalized weighted median 0.001 0.001 0.000 0.003 0.135
##
## IVW 0.001 0.001 0.000 0.003 0.016
## Penalized IVW 0.001 0.001 0.000 0.003 0.016
## Robust IVW 0.001 0.001 0.000 0.002 0.004
## Penalized robust IVW 0.001 0.001 0.000 0.002 0.004
##
## MR-Egger 0.001 0.002 -0.002 0.005 0.395
## (intercept) 0.000 0.000 0.000 0.000 0.974
## Penalized MR-Egger 0.001 0.002 -0.002 0.005 0.395
## (intercept) 0.000 0.000 0.000 0.000 0.974
## Robust MR-Egger 0.001 0.001 -0.001 0.004 0.286
## (intercept) 0.000 0.000 0.000 0.000 0.993
## Penalized robust MR-Egger 0.001 0.001 -0.001 0.004 0.286
## (intercept) 0.000 0.000 0.000 0.000 0.993
| id.exposure | id.outcome | exposure | outcome | snp_r2.exposure | snp_r2.outcome | correct_causal_direction | steiger_pval |
|---|---|---|---|---|---|---|---|
| JI02GY | hk2Grt | exposure | outcome | 0.0096945 | 3.9e-05 | TRUE | 0 |
## $r2_exp
## [1] 0
##
## $r2_out
## [1] 0.25
##
## $r2_exp_adj
## [1] 0
##
## $r2_out_adj
## [1] 0.25
##
## $correct_causal_direction
## [1] FALSE
##
## $steiger_test
## [1] 0
##
## $correct_causal_direction_adj
## [1] FALSE
##
## $steiger_test_adj
## [1] 0
##
## $vz
## [1] NaN
##
## $vz0
## [1] 0
##
## $vz1
## [1] NaN
##
## $sensitivity_ratio
## [1] NaN
##
## $sensitivity_plot
MRraps package
## $beta.hat
## [1] 0.001502448
##
## $beta.se
## [1] 0.0006337508
##
## $beta.p.value
## [1] 0.01775326
##
## $naive.se
## [1] 0.0006293192
##
## $chi.sq.test
## [1] 8.72018## over.dispersion loss.function beta.hat beta.se
## 1 FALSE l2 0.001502448 0.0006337508
## 2 FALSE huber 0.001502448 0.0006502142
## 3 FALSE tukey 0.001490996 0.0006501873
## 4 TRUE l2 0.001505703 0.0007133709
## 5 TRUE huber 0.001504387 0.0006502470
## 6 TRUE tukey 0.001492426 0.0006502194##
## MR-Lasso method
##
## Number of variants : 28
## Number of valid instruments : 28
## Tuning parameter : 0.1920885
## ------------------------------------------------------------------
## Exposure Estimate Std Error 95% CI p-value
## exposure 0.001 0.001 0.000, 0.003 0.016
## ------------------------------------------------------------------##
## Constrained maximum likelihood method (MRcML)
## Number of Variants: 28
## Results for: cML-MA-BIC
## ------------------------------------------------------------------
## Method Estimate SE Pvalue 95% CI
## cML-MA-BIC 0.002 0.001 0.016 [0.000,0.003]
## ------------------------------------------------------------------##
## Debiased inverse-variance weighted method
## (Over.dispersion:TRUE)
##
## Number of Variants : 28
## ------------------------------------------------------------------
## Method Estimate Std Error 95% CI p-value Condition
## dIVW 0.002 0.001 0.000, 0.003 0.016 385.443
## ------------------------------------------------------------------##
## Mode-based method of Hartwig et al
## (weighted, delta standard errors [not assuming NOME], bandwidth factor = 1)
##
## Number of Variants : 28
## ------------------------------------------------------------------
## Method Estimate Std Error 95% CI p-value
## MBE 0.001 0.002 -0.002, 0.004 0.521
## ------------------------------------------------------------------
DBP on BC
Introduction
Title: Investigating the causality between DBP on BC
- Exposure: DBP, GWAS summary statistics: OpenGWAS | Reference paper: Evangelou E et al., 2018
- Sample size: 757,601
- Ancestry: European
- Outcome: BC, GWAS summary statistics: University of Bristol | Reference paper: Burrows K et al., 2017
- Sample size:373,297 , Number of cases:1,279 , Number of controls: 372,016
- Ancestry: European
Data Preparation
1- Number of total SNPs in exposure: 7,160,619 SNPs
2- Number of SNPs exposure with p-value < \(5 \times 10^{-8}\): 83,547 SNPs
3- Number of SNPs exposure after clumping : 455 SNPs
4- Number of total SNPs in outcome: 9,904,926 SNPs
5- Number of common variants between exposure and outcome: 455 SNPs
6- Number of SNPs after harmonization (action=2) = 446 SNPs
(rs11664194, rs12321, rs1528293, rs3802517, rs61912333, rs710249, rs7694000, rs9893005, rs990619 being palindromic and were removed)
Checking weakness of the instruments:
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 29.65 38.96 51.43 79.45 82.04 815.82How many SNPs have been eliminated with checking the weakness: 0 SNP
RUN an initial MR:
## id.exposure id.outcome outcome exposure method nsnp
## 1 hk2Grt hk2Grt outcome exposure MR Egger 446
## 2 hk2Grt hk2Grt outcome exposure Weighted median 446
## 3 hk2Grt hk2Grt outcome exposure Inverse variance weighted 446
## 4 hk2Grt hk2Grt outcome exposure Simple mode 446
## 5 hk2Grt hk2Grt outcome exposure Weighted mode 446
## b se pval
## 1 1.584565e-04 1.108474e-04 0.15356334
## 2 9.376863e-05 6.812295e-05 0.16867871
## 3 9.844204e-05 4.549784e-05 0.03049015
## 4 -1.233739e-05 2.139253e-04 0.95403618
## 5 6.068265e-05 1.569924e-04 0.69928713
## id.exposure id.outcome outcome exposure method Q
## 1 hk2Grt hk2Grt outcome exposure MR Egger 542.9292
## 2 hk2Grt hk2Grt outcome exposure Inverse variance weighted 543.3604
## Q_df Q_pval
## 1 444 0.0008949034
## 2 445 0.0009569186## id.exposure id.outcome outcome exposure egger_intercept se
## 1 hk2Grt hk2Grt outcome exposure -1.202335e-05 2.024738e-05
## pval
## 1 0.5529333
Testing Outlier with PRESSO test
## $`Main MR results`
## Exposure MR Analysis Causal Estimate Sd T-stat
## 1 beta.exposure Raw 9.844204e-05 4.549784e-05 2.163664
## 2 beta.exposure Outlier-corrected 1.051567e-04 4.504968e-05 2.334239
## P-value
## 1 0.03102167
## 2 0.02002836
##
## $`MR-PRESSO results`
## $`MR-PRESSO results`$`Global Test`
## $`MR-PRESSO results`$`Global Test`$RSSobs
## [1] 545.9811
##
## $`MR-PRESSO results`$`Global Test`$Pvalue
## [1] 0.001
##
##
## $`MR-PRESSO results`$`Outlier Test`
## RSSobs Pvalue
## 1 3.494752e-08 1
## 2 1.122266e-10 1
## 3 6.238668e-10 1
## 4 1.051785e-08 1
## 5 1.470111e-07 1
## 6 4.335494e-08 1
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##
## $`MR-PRESSO results`$`Distortion Test`
## $`MR-PRESSO results`$`Distortion Test`$`Outliers Indices`
## [1] 104
##
## $`MR-PRESSO results`$`Distortion Test`$`Distortion Coefficient`
## beta.exposure
## -6.385405
##
## $`MR-PRESSO results`$`Distortion Test`$Pvalue
## [1] 0.89Radial test
##
## Radial IVW
##
## Estimate Std.Error t value Pr(>|t|)
## Effect (Mod.2nd) 9.844203e-05 4.549784e-05 2.163664 0.03049016
## Iterative 9.844204e-05 4.549784e-05 2.163664 0.03049015
## Exact (FE) 9.305751e-05 4.117733e-05 2.259921 0.02382614
## Exact (RE) 9.971526e-05 4.555699e-05 2.188803 0.02913015
##
##
## Residual standard error: 1.105 on 445 degrees of freedom
##
## F-statistic: 4.68 on 1 and 445 DF, p-value: 0.031
## Q-Statistic for heterogeneity: 543.2727 on 445 DF , p-value: 0.0009652871
##
## No significant outliers
## Number of iterations = 1## [1] "No significant outliers"Studentized residuals:
Cook’s distance
In statistics, Cook’s distance or Cook’s D is a commonly used estimate of the influence of a data point when performing a least-squares regression analysis.[1] In a practical ordinary least squares analysis, Cook’s distance can be used in several ways:
1- To indicate influential data points that are particularly worth checking for validity.
2- To indicate regions of the design space where it would be good to be able to obtain more data points. It is named after the American statistician R. Dennis Cook, who introduced the concept in 1977(Refernce).
Potential Outliers and Influential SNPs
## 7 24 30 56 103 117 124
## 0.01269078 0.07162858 0.02476856 0.03050298 0.02209659 0.08328175 0.05693010
## 129 147 149 174 214 226 294
## 0.02332969 0.08542978 0.06992192 0.01648396 0.01123118 0.03464593 0.03373624
## 307 358 367 374 384 388 395
## 0.07010790 0.02261226 0.04054549 0.02378892 0.04476658 0.23953629 0.05763937## [1] 5 7 11 24 25 30 92 104 105 117 124 129 147 149 174 213 245 259 294
## [20] 297 307 316 365 384 388 395 424report After Deleting Influential SNPs:
## id.exposure id.outcome outcome exposure method nsnp
## 1 hk2Grt hk2Grt outcome exposure MR Egger 407
## 2 hk2Grt hk2Grt outcome exposure Weighted median 407
## 3 hk2Grt hk2Grt outcome exposure Inverse variance weighted 407
## 4 hk2Grt hk2Grt outcome exposure Simple mode 407
## 5 hk2Grt hk2Grt outcome exposure Weighted mode 407
## b se pval
## 1 1.235639e-04 1.205534e-04 0.305988258
## 2 9.377856e-05 7.055939e-05 0.183823989
## 3 1.186416e-04 4.584136e-05 0.009650931
## 4 1.414102e-05 2.020524e-04 0.944238537
## 5 5.938085e-05 1.397076e-04 0.671035221
## id.exposure id.outcome outcome exposure method Q
## 1 hk2Grt hk2Grt outcome exposure MR Egger 360.4895
## 2 hk2Grt hk2Grt outcome exposure Inverse variance weighted 360.4914
## Q_df Q_pval
## 1 405 0.9453739
## 2 406 0.9492179## id.exposure id.outcome outcome exposure egger_intercept se
## 1 hk2Grt hk2Grt outcome exposure -9.153322e-07 2.073397e-05
## pval
## 1 0.9648094
OR report:
## id.exposure id.outcome outcome exposure method nsnp
## 1 hk2Grt hk2Grt outcome exposure MR Egger 407
## 2 hk2Grt hk2Grt outcome exposure Weighted median 407
## 3 hk2Grt hk2Grt outcome exposure Inverse variance weighted 407
## 4 hk2Grt hk2Grt outcome exposure Simple mode 407
## 5 hk2Grt hk2Grt outcome exposure Weighted mode 407
## b se pval lo_ci up_ci or
## 1 1.235639e-04 1.205534e-04 0.305988258 -1.127208e-04 0.0003598485 1.000124
## 2 9.377856e-05 7.055939e-05 0.183823989 -4.451785e-05 0.0002320750 1.000094
## 3 1.186416e-04 4.584136e-05 0.009650931 2.879257e-05 0.0002084907 1.000119
## 4 1.414102e-05 2.020524e-04 0.944238537 -3.818817e-04 0.0004101638 1.000014
## 5 5.938085e-05 1.397076e-04 0.671035221 -2.144461e-04 0.0003332078 1.000059
## or_lci95 or_uci95
## 1 0.9998873 1.000360
## 2 0.9999555 1.000232
## 3 1.0000288 1.000209
## 4 0.9996182 1.000410
## 5 0.9997856 1.000333MendelianRandomization Package
##
## Inverse-variance weighted method
## (variants uncorrelated, random-effect model)
##
## Number of Variants : 407
##
## ------------------------------------------------------------------
## Method Estimate Std Error 95% CI p-value
## IVW 0.000 0.000 0.000, 0.000 0.010
## ------------------------------------------------------------------
## Residual standard error = 0.942
## Residual standard error is set to 1 in calculation of confidence interval when its estimate is less than 1.
## Heterogeneity test statistic (Cochran's Q) = 360.4914 on 406 degrees of freedom, (p-value = 0.9492). I^2 = 0.0%.
## F statistic = 70.2.## Method Estimate Std Error 95% CI P-value
## Simple median 0.000 0.000 0.000 0.000 0.312
## Weighted median 0.000 0.000 0.000 0.000 0.185
## Penalized weighted median 0.000 0.000 0.000 0.000 0.212
##
## IVW 0.000 0.000 0.000 0.000 0.010
## Penalized IVW 0.000 0.000 0.000 0.000 0.012
## Robust IVW 0.000 0.000 0.000 0.000 0.018
## Penalized robust IVW 0.000 0.000 0.000 0.000 0.018
##
## MR-Egger 0.000 0.000 0.000 0.000 0.305
## (intercept) 0.000 0.000 0.000 0.000 0.965
## Penalized MR-Egger 0.000 0.000 0.000 0.000 0.281
## (intercept) 0.000 0.000 0.000 0.000 0.902
## Robust MR-Egger 0.000 0.000 0.000 0.000 0.097
## (intercept) 0.000 0.000 0.000 0.000 0.612
## Penalized robust MR-Egger 0.000 0.000 0.000 0.000 0.096
## (intercept) 0.000 0.000 0.000 0.000 0.609
| id.exposure | id.outcome | exposure | outcome | snp_r2.exposure | snp_r2.outcome | correct_causal_direction | steiger_pval |
|---|---|---|---|---|---|---|---|
| hk2Grt | hk2Grt | exposure | outcome | 0.0376853 | 0.0009837 | TRUE | 0 |
## $r2_exp
## [1] 0
##
## $r2_out
## [1] 0.25
##
## $r2_exp_adj
## [1] 0
##
## $r2_out_adj
## [1] 0.25
##
## $correct_causal_direction
## [1] FALSE
##
## $steiger_test
## [1] 0
##
## $correct_causal_direction_adj
## [1] FALSE
##
## $steiger_test_adj
## [1] 0
##
## $vz
## [1] NaN
##
## $vz0
## [1] 0
##
## $vz1
## [1] NaN
##
## $sensitivity_ratio
## [1] NaN
##
## $sensitivity_plot
MRraps package
## $beta.hat
## [1] 0.0001201561
##
## $beta.se
## [1] 4.654834e-05
##
## $beta.p.value
## [1] 0.009842361
##
## $naive.se
## [1] 4.62152e-05
##
## $chi.sq.test
## [1] 360.4059## over.dispersion loss.function beta.hat beta.se
## 1 FALSE l2 0.0001201561 4.654834e-05
## 2 FALSE huber 0.0001065602 4.775510e-05
## 3 FALSE tukey 0.0001048152 4.775490e-05
## 4 TRUE l2 0.0001187222 5.359789e-05
## 5 TRUE huber 0.0001070403 4.775532e-05
## 6 TRUE tukey 0.0001065842 4.775534e-05##
## MR-Lasso method
##
## Number of variants : 407
## Number of valid instruments : 407
## Tuning parameter : 0.1338801
## ------------------------------------------------------------------
## Exposure Estimate Std Error 95% CI p-value
## exposure 0.000 0.000 0.000, 0.000 0.010
## ------------------------------------------------------------------##
## Constrained maximum likelihood method (MRcML)
## Number of Variants: 407
## Results for: cML-MA-BIC
## ------------------------------------------------------------------
## Method Estimate SE Pvalue 95% CI
## cML-MA-BIC 0.000 0.000 0.009 [0.000,0.000]
## ------------------------------------------------------------------##
## Debiased inverse-variance weighted method
## (Over.dispersion:TRUE)
##
## Number of Variants : 407
## ------------------------------------------------------------------
## Method Estimate Std Error 95% CI p-value Condition
## dIVW 0.000 0.000 0.000, 0.000 0.010 1395.739
## ------------------------------------------------------------------##
## Mode-based method of Hartwig et al
## (weighted, delta standard errors [not assuming NOME], bandwidth factor = 1)
##
## Number of Variants : 407
## ------------------------------------------------------------------
## Method Estimate Std Error 95% CI p-value
## MBE 0.000 0.000 0.000, 0.000 0.597
## ------------------------------------------------------------------
Hypertension on BC
Introduction
Title: Investigating the causality between HBP on BC
- Exposure: Hypertension, GWAS summary statistics: OpenGWAS | Reference paper: Elsworth B et al., 2018
- Sample size: 462,933 , Number of
cases: 119,731 , Number of controls:
343,202
- Ancestry: European
- Outcome: BC, GWAS summary statistics: University of Bristol | Reference paper: Burrows K et al., 2017
- Sample size:373,297 , Number of cases:1,279 , Number of controls: 372,016
- Ancestry: European
Data Preparation
1- Number of total SNPs in exposure: 9,851,867 SNPs
2- Number of SNPs exposure with p-value < \(5 \times 10^{-8}\): 24,844 SNPs
3- Number of SNPs exposure after clumping : 225 SNPs
4- Number of total SNPs in outcome: 9,904,926 SNPs
5- Number of common variants between exposure and outcome: 205 SNPs
6- Number of SNPs after harmonization (action=2) = 199 SNPs
(rs10786156, rs10995311, rs2046645, rs6926537, rs7171632, rs7310615 being palindromic and were removed)
Checking weakness of the instruments:
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 29.76 35.42 44.79 60.20 62.88 462.71How many SNPs have been eliminated with checking the weakness: 0 SNP
RUN an initial MR:
## id.exposure id.outcome outcome exposure method nsnp
## 1 MfEccK hk2Grt outcome exposure MR Egger 199
## 2 MfEccK hk2Grt outcome exposure Weighted median 199
## 3 MfEccK hk2Grt outcome exposure Inverse variance weighted 199
## 4 MfEccK hk2Grt outcome exposure Simple mode 199
## 5 MfEccK hk2Grt outcome exposure Weighted mode 199
## b se pval
## 1 -0.001269811 0.004257412 0.7658199
## 2 0.001860200 0.002137132 0.3840715
## 3 0.001668861 0.001510451 0.2692132
## 4 0.004750532 0.006187746 0.4435608
## 5 0.004750532 0.004989320 0.3421867
## id.exposure id.outcome outcome exposure method Q
## 1 MfEccK hk2Grt outcome exposure MR Egger 237.5138
## 2 MfEccK hk2Grt outcome exposure Inverse variance weighted 238.1711
## Q_df Q_pval
## 1 197 0.02565384
## 2 198 0.02684607## id.exposure id.outcome outcome exposure egger_intercept se pval
## 1 MfEccK hk2Grt outcome exposure 2.55375e-05 3.45851e-05 0.4611525
Testing Outlier with PRESSO test
## $`Main MR results`
## Exposure MR Analysis Causal Estimate Sd T-stat
## 1 beta.exposure Raw 0.001668861 0.001510451 1.1048763
## 2 beta.exposure Outlier-corrected 0.001405855 0.001476902 0.9518946
## P-value
## 1 0.2705540
## 2 0.3423168
##
## $`MR-PRESSO results`
## $`MR-PRESSO results`$`Global Test`
## $`MR-PRESSO results`$`Global Test`$RSSobs
## [1] 240.5841
##
## $`MR-PRESSO results`$`Global Test`$Pvalue
## [1] 0.029
##
##
## $`MR-PRESSO results`$`Outlier Test`
## RSSobs Pvalue
## 1 7.517691e-08 1
## 2 1.271457e-11 1
## 3 8.992182e-08 1
## 4 6.527456e-09 1
## 5 3.302688e-09 1
## 6 1.348771e-08 1
## 7 7.440307e-09 1
## 8 5.546649e-10 1
## 9 3.157258e-08 1
## 10 7.436410e-08 1
## 11 2.026015e-08 1
## 12 6.089736e-08 1
## 13 8.226630e-09 1
## 14 3.245455e-08 1
## 15 1.113986e-09 1
## 16 1.989723e-08 1
## 17 1.176837e-09 1
## 18 1.444003e-08 1
## 19 6.216653e-09 1
## 20 1.387624e-07 1
## 21 5.826380e-09 1
## 22 1.780977e-09 1
## 23 2.522604e-08 1
## 24 1.262028e-07 1
## 25 8.277351e-08 1
## 26 6.313185e-11 1
## 27 2.039514e-08 1
## 28 8.460995e-08 1
## 29 1.299840e-08 1
## 30 4.431577e-08 1
## 31 2.858516e-08 1
## 32 9.396671e-08 1
## 33 1.287885e-07 1
## 34 6.825920e-09 1
## 35 1.771519e-08 1
## 36 1.017379e-10 1
## 37 2.895997e-08 1
## 38 7.929748e-10 1
## 39 3.947904e-08 1
## 40 3.352432e-08 1
## 41 2.366309e-08 1
## 42 1.266446e-07 1
## 43 3.923154e-09 1
## 44 3.954464e-08 1
## 45 9.792375e-08 1
## 46 5.811787e-08 1
## 47 1.876018e-10 1
## 48 4.631179e-09 1
## 49 3.697454e-08 1
## 50 5.768256e-09 1
## 51 3.085578e-08 1
## 52 2.272024e-07 1
## 53 3.862546e-08 1
## 54 9.645274e-10 1
## 55 5.145913e-09 1
## 56 2.789418e-08 1
## 57 3.248783e-09 1
## 58 1.057350e-08 1
## 59 2.029285e-09 1
## 60 6.770080e-09 1
## 61 8.958385e-08 1
## 62 5.016072e-07 1
## 63 4.424039e-08 1
## 64 1.722991e-09 1
## 65 1.422302e-08 1
## 66 4.673635e-08 1
## 67 2.283582e-10 1
## 68 4.867976e-09 1
## 69 6.387049e-08 1
## 70 1.302530e-14 1
## 71 2.193830e-10 1
## 72 3.168007e-09 1
## 73 1.540658e-10 1
## 74 1.886432e-09 1
## 75 3.298590e-09 1
## 76 3.169772e-09 1
## 77 6.138605e-08 1
## 78 3.424400e-10 1
## 79 2.521307e-11 1
## 80 9.267750e-08 1
## 81 5.244286e-09 1
## 82 5.566801e-10 1
## 83 1.026163e-08 1
## 84 1.613211e-07 1
## 85 9.643017e-09 1
## 86 1.553503e-07 1
## 87 4.414635e-08 1
## 88 2.028242e-09 1
## 89 6.157915e-08 1
## 90 6.013710e-10 1
## 91 9.645818e-08 1
## 92 1.193181e-08 1
## 93 4.207485e-08 1
## 94 1.601974e-08 1
## 95 2.573316e-08 1
## 96 1.057498e-08 1
## 97 7.371938e-09 1
## 98 1.561171e-08 1
## 99 1.688617e-08 1
## 100 4.647174e-12 1
## 101 3.871144e-08 1
## 102 7.966858e-09 1
## 103 2.603926e-09 1
## 104 1.226622e-09 1
## 105 4.260486e-09 1
## 106 5.755723e-08 1
## 107 1.775891e-09 1
## 108 8.019706e-08 1
## 109 1.085389e-11 1
## 110 1.161823e-07 1
## 111 1.714215e-09 1
## 112 5.381390e-09 1
## 113 4.406567e-08 1
## 114 8.216829e-09 1
## 115 1.217072e-08 1
## 116 1.448906e-08 1
## 117 3.899343e-11 1
## 118 3.542305e-08 1
## 119 4.058911e-08 1
## 120 7.351878e-08 1
## 121 2.734764e-08 1
## 122 5.098990e-10 1
## 123 4.378023e-08 1
## 124 4.252995e-08 1
## 125 8.384509e-09 1
## 126 6.068484e-10 1
## 127 1.961639e-07 1
## 128 1.650664e-08 1
## 129 2.375269e-09 1
## 130 1.070594e-07 1
## 131 6.268891e-08 1
## 132 1.241526e-08 1
## 133 5.345562e-08 1
## 134 2.606111e-08 1
## 135 2.629170e-10 1
## 136 2.415578e-08 1
## 137 1.517659e-08 1
## 138 1.733583e-08 1
## 139 2.878326e-09 1
## 140 5.497251e-10 1
## 141 1.052341e-08 1
## 142 8.026045e-09 1
## 143 3.003803e-08 1
## 144 6.927187e-08 1
## 145 6.952417e-08 1
## 146 2.169303e-08 1
## 147 4.649198e-09 1
## 148 5.891687e-09 1
## 149 7.639013e-09 1
## 150 3.400453e-09 1
## 151 6.171273e-09 1
## 152 8.749325e-08 1
## 153 3.003729e-10 1
## 154 2.030090e-10 1
## 155 6.739578e-07 <0.199
## 156 5.608521e-09 1
## 157 4.727435e-09 1
## 158 3.719203e-09 1
## 159 9.673984e-08 1
## 160 6.731137e-08 1
## 161 4.432076e-08 1
## 162 1.213806e-08 1
## 163 1.176652e-08 1
## 164 5.929749e-09 1
## 165 4.164943e-10 1
## 166 1.110464e-08 1
## 167 2.333890e-10 1
## 168 2.996059e-08 1
## 169 3.602197e-07 1
## 170 1.195177e-08 1
## 171 8.589169e-08 1
## 172 1.584854e-08 1
## 173 1.712310e-10 1
## 174 5.338408e-08 1
## 175 9.580536e-09 1
## 176 4.129467e-08 1
## 177 1.148222e-08 1
## 178 3.271415e-08 1
## 179 1.141810e-08 1
## 180 1.209353e-07 1
## 181 3.762199e-08 1
## 182 3.344149e-08 1
## 183 2.122518e-09 1
## 184 1.860690e-10 1
## 185 3.673720e-09 1
## 186 9.075614e-08 1
## 187 3.876631e-08 1
## 188 1.040749e-11 1
## 189 1.568734e-08 1
## 190 8.114803e-09 1
## 191 6.725634e-09 1
## 192 8.631564e-08 1
## 193 4.797815e-09 1
## 194 3.824765e-08 1
## 195 2.468899e-11 1
## 196 1.589328e-08 1
## 197 7.021538e-11 1
## 198 9.353807e-08 1
## 199 1.628477e-08 1
##
## $`MR-PRESSO results`$`Distortion Test`
## $`MR-PRESSO results`$`Distortion Test`$`Outliers Indices`
## [1] 155
##
## $`MR-PRESSO results`$`Distortion Test`$`Distortion Coefficient`
## beta.exposure
## 18.7079
##
## $`MR-PRESSO results`$`Distortion Test`$Pvalue
## [1] 0.816Radial test
##
## Radial IVW
##
## Estimate Std.Error t value Pr(>|t|)
## Effect (Mod.2nd) 0.001668861 0.001510451 1.104876 0.2692133
## Iterative 0.001668861 0.001510451 1.104876 0.2692133
## Exact (FE) 0.001691148 0.001377279 1.227890 0.2194881
## Exact (RE) 0.001697580 0.001547802 1.096768 0.2740749
##
##
## Residual standard error: 1.097 on 198 degrees of freedom
##
## F-statistic: 1.22 on 1 and 198 DF, p-value: 0.271
## Q-Statistic for heterogeneity: 238.1419 on 198 DF , p-value: 0.02692668
##
## No significant outliers
## Number of iterations = 2## [1] "No significant outliers"Studentized residuals:
Cook’s distance
In statistics, Cook’s distance or Cook’s D is a commonly used estimate of the influence of a data point when performing a least-squares regression analysis.[1] In a practical ordinary least squares analysis, Cook’s distance can be used in several ways:
1- To indicate influential data points that are particularly worth checking for validity.
2- To indicate regions of the design space where it would be good to be able to obtain more data points. It is named after the American statistician R. Dennis Cook, who introduced the concept in 1977(Refernce).
Potential Outliers and Influential SNPs
## 24 52 62 86 91 127 155
## 0.07184201 0.03890703 0.12925860 0.15149717 0.04250918 0.11267649 0.08524017
## 159 169
## 0.03709560 0.16263814## [1] 20 52 62 84 86 127 155 169report After Deleting Influential SNPs:
## id.exposure id.outcome outcome exposure method nsnp
## 1 MfEccK hk2Grt outcome exposure MR Egger 167
## 2 MfEccK hk2Grt outcome exposure Weighted median 167
## 3 MfEccK hk2Grt outcome exposure Inverse variance weighted 167
## 4 MfEccK hk2Grt outcome exposure Simple mode 167
## 5 MfEccK hk2Grt outcome exposure Weighted mode 167
## b se pval
## 1 0.0010196479 0.004707716 0.8287948
## 2 0.0008035741 0.002325282 0.7296573
## 3 -0.0004145744 0.001576751 0.7926049
## 4 0.0051598515 0.006219085 0.4079112
## 5 0.0038014567 0.004411757 0.3901149
## id.exposure id.outcome outcome exposure method Q
## 1 MfEccK hk2Grt outcome exposure MR Egger 106.5795
## 2 MfEccK hk2Grt outcome exposure Inverse variance weighted 106.6840
## Q_df Q_pval
## 1 165 0.9998751
## 2 166 0.9998979## id.exposure id.outcome outcome exposure egger_intercept se
## 1 MfEccK hk2Grt outcome exposure -1.186155e-05 3.668582e-05
## pval
## 1 0.7468564
OR report:
## id.exposure id.outcome outcome exposure method nsnp
## 1 MfEccK hk2Grt outcome exposure MR Egger 167
## 2 MfEccK hk2Grt outcome exposure Weighted median 167
## 3 MfEccK hk2Grt outcome exposure Inverse variance weighted 167
## 4 MfEccK hk2Grt outcome exposure Simple mode 167
## 5 MfEccK hk2Grt outcome exposure Weighted mode 167
## b se pval lo_ci up_ci or
## 1 0.0010196479 0.004707716 0.8287948 -0.008207475 0.010246771 1.0010202
## 2 0.0008035741 0.002325282 0.7296573 -0.003753978 0.005361126 1.0008039
## 3 -0.0004145744 0.001576751 0.7926049 -0.003505006 0.002675857 0.9995855
## 4 0.0051598515 0.006219085 0.4079112 -0.007029555 0.017349258 1.0051732
## 5 0.0038014567 0.004411757 0.3901149 -0.004845587 0.012448501 1.0038087
## or_lci95 or_uci95
## 1 0.9918261 1.010299
## 2 0.9962531 1.005376
## 3 0.9965011 1.002679
## 4 0.9929951 1.017501
## 5 0.9951661 1.012526MendelianRandomization Package
##
## Inverse-variance weighted method
## (variants uncorrelated, random-effect model)
##
## Number of Variants : 167
##
## ------------------------------------------------------------------
## Method Estimate Std Error 95% CI p-value
## IVW 0.000 0.002 -0.004, 0.003 0.793
## ------------------------------------------------------------------
## Residual standard error = 0.802
## Residual standard error is set to 1 in calculation of confidence interval when its estimate is less than 1.
## Heterogeneity test statistic (Cochran's Q) = 106.6840 on 166 degrees of freedom, (p-value = 0.9999). I^2 = 0.0%.
## F statistic = 54.7.## Method Estimate Std Error 95% CI P-value
## Simple median 0.001 0.002 -0.004 0.005 0.763
## Weighted median 0.001 0.002 -0.004 0.005 0.729
## Penalized weighted median 0.001 0.002 -0.004 0.005 0.712
##
## IVW 0.000 0.002 -0.004 0.003 0.793
## Penalized IVW 0.000 0.002 -0.004 0.003 0.793
## Robust IVW 0.000 0.001 -0.003 0.002 0.807
## Penalized robust IVW 0.000 0.001 -0.003 0.002 0.807
##
## MR-Egger 0.001 0.005 -0.008 0.010 0.829
## (intercept) 0.000 0.000 0.000 0.000 0.746
## Penalized MR-Egger 0.001 0.005 -0.008 0.010 0.829
## (intercept) 0.000 0.000 0.000 0.000 0.746
## Robust MR-Egger 0.001 0.004 -0.006 0.008 0.760
## (intercept) 0.000 0.000 0.000 0.000 0.697
## Penalized robust MR-Egger 0.001 0.004 -0.006 0.008 0.760
## (intercept) 0.000 0.000 0.000 0.000 0.697
| id.exposure | id.outcome | exposure | outcome | snp_r2.exposure | snp_r2.outcome | correct_causal_direction | steiger_pval |
|---|---|---|---|---|---|---|---|
| MfEccK | hk2Grt | exposure | outcome | 0.0197378 | 0.0002854 | TRUE | 0 |
## $r2_exp
## [1] 0
##
## $r2_out
## [1] 0.25
##
## $r2_exp_adj
## [1] 0
##
## $r2_out_adj
## [1] 0.25
##
## $correct_causal_direction
## [1] FALSE
##
## $steiger_test
## [1] 0
##
## $correct_causal_direction_adj
## [1] FALSE
##
## $steiger_test_adj
## [1] 0
##
## $vz
## [1] NaN
##
## $vz0
## [1] 0
##
## $vz1
## [1] NaN
##
## $sensitivity_ratio
## [1] NaN
##
## $sensitivity_plot
MRraps package
## $beta.hat
## [1] -0.0004194714
##
## $beta.se
## [1] 0.001611633
##
## $beta.p.value
## [1] 0.7946499
##
## $naive.se
## [1] 0.001596741
##
## $chi.sq.test
## [1] 106.6832## over.dispersion loss.function beta.hat beta.se
## 1 FALSE l2 -0.0004194714 0.001611633
## 2 FALSE huber -0.0004355307 0.001653500
## 3 FALSE tukey -0.0003694527 0.001653499
## 4 TRUE l2 -0.0004078740 0.001861652
## 5 TRUE huber -0.0004353488 0.001653500
## 6 TRUE tukey -0.0003696686 0.001653500##
## MR-Lasso method
##
## Number of variants : 167
## Number of valid instruments : 167
## Tuning parameter : 0.1614645
## ------------------------------------------------------------------
## Exposure Estimate Std Error 95% CI p-value
## exposure 0.000 0.002 -0.004, 0.003 0.793
## ------------------------------------------------------------------##
## Constrained maximum likelihood method (MRcML)
## Number of Variants: 167
## Results for: cML-MA-BIC
## ------------------------------------------------------------------
## Method Estimate SE Pvalue 95% CI
## cML-MA-BIC 0.000 0.002 0.793 [-0.004,0.003]
## ------------------------------------------------------------------##
## Debiased inverse-variance weighted method
## (Over.dispersion:TRUE)
##
## Number of Variants : 167
## ------------------------------------------------------------------
## Method Estimate Std Error 95% CI p-value Condition
## dIVW 0.000 0.002 -0.004, 0.003 0.793 694.209
## ------------------------------------------------------------------##
## Mode-based method of Hartwig et al
## (weighted, delta standard errors [not assuming NOME], bandwidth factor = 1)
##
## Number of Variants : 167
## ------------------------------------------------------------------
## Method Estimate Std Error 95% CI p-value
## MBE 0.004 0.004 -0.005, 0.012 0.388
## ------------------------------------------------------------------
SBP on BC
Introduction
Title: Investigating the causality between SBP on BC
- Exposure: SBP, GWAS summary statistics: OpenGWAS | Reference paper: Evangelou E et al., 2018
- Sample size: 757,601
- Ancestry: European
- Outcome: BC, GWAS summary statistics: University of Bristol | Reference paper: Burrows K et al., 2017
- Sample size:373,297 , Number of cases:1,279 , Number of controls: 372,016
- Ancestry: European
Data Preparation
1- Number of total SNPs in exposure: 7,088,083 SNPs
2- Number of SNPs exposure with p-value < \(5 \times 10^{-8}\): 74,125 SNPs
3- Number of SNPs exposure after clumping : 456 SNPs
4- Number of total SNPs in outcome: 9,904,926 SNPs
5- Number of common variants between exposure and outcome: 456 SNPs
6- Number of SNPs after harmonization (action=2) = 441 SNPs
(rs1012089, rs11585169, rs11967262, rs12321, rs17610485, rs1870735, rs2024385, rs3802517, rs3828282, rs3845811, rs4834792, rs7310615, rs7463212, rs7796, rs961764 being palindromic and were removed)
Checking weakness of the instruments:
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 29.72 38.08 50.39 75.07 76.22 627.55How many SNPs have been eliminated with checking the weakness: 0 SNP
RUN an initial MR:
## id.exposure id.outcome outcome exposure method nsnp
## 1 ufy4y1 hk2Grt outcome exposure MR Egger 441
## 2 ufy4y1 hk2Grt outcome exposure Weighted median 441
## 3 ufy4y1 hk2Grt outcome exposure Inverse variance weighted 441
## 4 ufy4y1 hk2Grt outcome exposure Simple mode 441
## 5 ufy4y1 hk2Grt outcome exposure Weighted mode 441
## b se pval
## 1 -2.253819e-05 6.467707e-05 0.7276523
## 2 -1.893980e-06 3.871551e-05 0.9609827
## 3 1.743286e-05 2.567725e-05 0.4971871
## 4 -6.396224e-05 1.222661e-04 0.6011403
## 5 -3.554654e-05 8.961968e-05 0.6918270
## id.exposure id.outcome outcome exposure method Q
## 1 ufy4y1 hk2Grt outcome exposure MR Egger 482.7800
## 2 ufy4y1 hk2Grt outcome exposure Inverse variance weighted 483.2787
## Q_df Q_pval
## 1 439 0.07305894
## 2 440 0.07550695## id.exposure id.outcome outcome exposure egger_intercept se
## 1 ufy4y1 hk2Grt outcome exposure 1.336164e-05 1.984127e-05
## pval
## 1 0.5010303
Testing Outlier with PRESSO test
## $`Main MR results`
## Exposure MR Analysis Causal Estimate Sd T-stat
## 1 beta.exposure Raw 1.743286e-05 2.567725e-05 0.6789223
## 2 beta.exposure Outlier-corrected NA NA NA
## P-value
## 1 0.4975441
## 2 NA
##
## $`MR-PRESSO results`
## $`MR-PRESSO results`$`Global Test`
## $`MR-PRESSO results`$`Global Test`$RSSobs
## [1] 485.438
##
## $`MR-PRESSO results`$`Global Test`$Pvalue
## [1] 0.078Radial test
##
## Radial IVW
##
## Estimate Std.Error t value Pr(>|t|)
## Effect (Mod.2nd) 1.743287e-05 2.567725e-05 0.6789228 0.4971868
## Iterative 1.743286e-05 2.567725e-05 0.6789223 0.4971871
## Exact (FE) 1.544891e-05 2.450071e-05 0.6305498 0.5283350
## Exact (RE) 3.259713e-05 3.499166e-05 0.9315685 0.3520704
##
##
## Residual standard error: 1.048 on 440 degrees of freedom
##
## F-statistic: 0.46 on 1 and 440 DF, p-value: 0.498
## Q-Statistic for heterogeneity: 483.2714 on 440 DF , p-value: 0.07554011
##
## No significant outliers
## Number of iterations = 1## [1] "No significant outliers"Studentized residuals:
Cook’s distance
In statistics, Cook’s distance or Cook’s D is a commonly used estimate of the influence of a data point when performing a least-squares regression analysis.[1] In a practical ordinary least squares analysis, Cook’s distance can be used in several ways:
1- To indicate influential data points that are particularly worth checking for validity.
2- To indicate regions of the design space where it would be good to be able to obtain more data points. It is named after the American statistician R. Dennis Cook, who introduced the concept in 1977(Refernce).
Potential Outliers and Influential SNPs
## 12 22 29 35 57 76 83
## 0.01759063 0.01069175 0.11242044 0.02534383 0.05728427 0.01457870 0.01426455
## 110 148 170 206 218 219 229
## 0.04941212 0.17537897 0.01758714 0.01072930 0.01509872 0.01899798 0.03924269
## 284 287 326 347 379 400 406
## 0.03989497 0.02942982 0.21102661 0.07100033 0.03452196 0.01242249 0.02355500## [1] 6 12 29 34 57 65 75 102 110 122 125 148 170 206 218 264 284 287 326
## [20] 347 354 379 385 400 406report After Deleting Influential SNPs:
## id.exposure id.outcome outcome exposure method nsnp
## 1 ufy4y1 hk2Grt outcome exposure MR Egger 408
## 2 ufy4y1 hk2Grt outcome exposure Weighted median 408
## 3 ufy4y1 hk2Grt outcome exposure Inverse variance weighted 408
## 4 ufy4y1 hk2Grt outcome exposure Simple mode 408
## 5 ufy4y1 hk2Grt outcome exposure Weighted mode 408
## b se pval
## 1 5.370326e-05 7.001831e-05 0.44353395
## 2 2.090026e-05 4.025492e-05 0.60362287
## 3 4.601377e-05 2.659357e-05 0.08358391
## 4 -4.264975e-05 1.148409e-04 0.71054699
## 5 -6.373503e-08 8.402062e-05 0.99939513
## id.exposure id.outcome outcome exposure method Q
## 1 ufy4y1 hk2Grt outcome exposure MR Egger 348.8775
## 2 ufy4y1 hk2Grt outcome exposure Inverse variance weighted 348.8916
## Q_df Q_pval
## 1 406 0.9813971
## 2 407 0.9829522## id.exposure id.outcome outcome exposure egger_intercept se
## 1 ufy4y1 hk2Grt outcome exposure -2.443788e-06 2.058497e-05
## pval
## 1 0.9055582
OR report:
## id.exposure id.outcome outcome exposure method nsnp
## 1 ufy4y1 hk2Grt outcome exposure MR Egger 408
## 2 ufy4y1 hk2Grt outcome exposure Weighted median 408
## 3 ufy4y1 hk2Grt outcome exposure Inverse variance weighted 408
## 4 ufy4y1 hk2Grt outcome exposure Simple mode 408
## 5 ufy4y1 hk2Grt outcome exposure Weighted mode 408
## b se pval lo_ci up_ci or
## 1 5.370326e-05 7.001831e-05 0.44353395 -8.353263e-05 1.909391e-04 1.0000537
## 2 2.090026e-05 4.025492e-05 0.60362287 -5.799938e-05 9.979990e-05 1.0000209
## 3 4.601377e-05 2.659357e-05 0.08358391 -6.109617e-06 9.813716e-05 1.0000460
## 4 -4.264975e-05 1.148409e-04 0.71054699 -2.677380e-04 1.824385e-04 0.9999574
## 5 -6.373503e-08 8.402062e-05 0.99939513 -1.647442e-04 1.646167e-04 0.9999999
## or_lci95 or_uci95
## 1 0.9999165 1.000191
## 2 0.9999420 1.000100
## 3 0.9999939 1.000098
## 4 0.9997323 1.000182
## 5 0.9998353 1.000165MendelianRandomization Package
##
## Inverse-variance weighted method
## (variants uncorrelated, random-effect model)
##
## Number of Variants : 408
##
## ------------------------------------------------------------------
## Method Estimate Std Error 95% CI p-value
## IVW 0.000 0.000 0.000, 0.000 0.084
## ------------------------------------------------------------------
## Residual standard error = 0.926
## Residual standard error is set to 1 in calculation of confidence interval when its estimate is less than 1.
## Heterogeneity test statistic (Cochran's Q) = 348.8916 on 407 degrees of freedom, (p-value = 0.9830). I^2 = 0.0%.
## F statistic = 68.8.## Method Estimate Std Error 95% CI P-value
## Simple median 0.000 0.000 0.000 0.000 0.555
## Weighted median 0.000 0.000 0.000 0.000 0.576
## Penalized weighted median 0.000 0.000 0.000 0.000 0.579
##
## IVW 0.000 0.000 0.000 0.000 0.084
## Penalized IVW 0.000 0.000 0.000 0.000 0.084
## Robust IVW 0.000 0.000 0.000 0.000 0.059
## Penalized robust IVW 0.000 0.000 0.000 0.000 0.059
##
## MR-Egger 0.000 0.000 0.000 0.000 0.443
## (intercept) 0.000 0.000 0.000 0.000 0.905
## Penalized MR-Egger 0.000 0.000 0.000 0.000 0.443
## (intercept) 0.000 0.000 0.000 0.000 0.905
## Robust MR-Egger 0.000 0.000 0.000 0.000 0.264
## (intercept) 0.000 0.000 0.000 0.000 0.802
## Penalized robust MR-Egger 0.000 0.000 0.000 0.000 0.264
## (intercept) 0.000 0.000 0.000 0.000 0.802
| id.exposure | id.outcome | exposure | outcome | snp_r2.exposure | snp_r2.outcome | correct_causal_direction | steiger_pval |
|---|---|---|---|---|---|---|---|
| ufy4y1 | hk2Grt | exposure | outcome | 0.0370454 | 0.0009415 | TRUE | 0 |
## $r2_exp
## [1] 0
##
## $r2_out
## [1] 0.25
##
## $r2_exp_adj
## [1] 0
##
## $r2_out_adj
## [1] 0.25
##
## $correct_causal_direction
## [1] FALSE
##
## $steiger_test
## [1] 0
##
## $correct_causal_direction_adj
## [1] FALSE
##
## $steiger_test_adj
## [1] 0
##
## $vz
## [1] NaN
##
## $vz0
## [1] 0
##
## $vz1
## [1] NaN
##
## $sensitivity_ratio
## [1] NaN
##
## $sensitivity_plot
MRraps package
## $beta.hat
## [1] 4.658926e-05
##
## $beta.se
## [1] 2.701764e-05
##
## $beta.p.value
## [1] 0.08463538
##
## $naive.se
## [1] 2.682018e-05
##
## $chi.sq.test
## [1] 348.8541## over.dispersion loss.function beta.hat beta.se
## 1 FALSE l2 4.658926e-05 2.701764e-05
## 2 FALSE huber 4.529768e-05 2.771934e-05
## 3 FALSE tukey 4.468224e-05 2.771931e-05
## 4 TRUE l2 4.786712e-05 2.996283e-05
## 5 TRUE huber 4.786712e-05 2.771972e-05
## 6 TRUE tukey 4.786712e-05 2.771977e-05##
## MR-Lasso method
##
## Number of variants : 408
## Number of valid instruments : 408
## Tuning parameter : 0.1151046
## ------------------------------------------------------------------
## Exposure Estimate Std Error 95% CI p-value
## exposure 0.000 0.000 0.000, 0.000 0.084
## ------------------------------------------------------------------##
## Constrained maximum likelihood method (MRcML)
## Number of Variants: 408
## Results for: cML-MA-BIC
## ------------------------------------------------------------------
## Method Estimate SE Pvalue 95% CI
## cML-MA-BIC 0.000 0.000 0.081 [0.000,0.000]
## ------------------------------------------------------------------##
## Debiased inverse-variance weighted method
## (Over.dispersion:TRUE)
##
## Number of Variants : 408
## ------------------------------------------------------------------
## Method Estimate Std Error 95% CI p-value Condition
## dIVW 0.000 0.000 0.000, 0.000 0.084 1369.568
## ------------------------------------------------------------------##
## Mode-based method of Hartwig et al
## (weighted, delta standard errors [not assuming NOME], bandwidth factor = 1)
##
## Number of Variants : 408
## ------------------------------------------------------------------
## Method Estimate Std Error 95% CI p-value
## MBE 0.000 0.000 0.000, 0.000 0.999
## ------------------------------------------------------------------
FBG on BC
Introduction
Title: Investigating the causality between FBS on BC
- Exposure: FBG, GWAS summary statistics: OpenGWAS | Reference paper: Mahajan A et al., 2015
- Sample size: 33,231
- Ancestry: European
- Outcome: BC, GWAS summary statistics: University of Bristol | Reference paper: Burrows K et al., 2017
- Sample size:373,297 , Number of cases:1,279 , Number of controls: 372,016
- Ancestry: European
Data Preparation
1- Number of total SNPs in exposure: 105,585 SNPs
2- Number of SNPs exposure with p-value < \(5 \times 10^{-5}\): 107 SNPs
3- Number of SNPs exposure after clumping : 80 SNPs
4- Number of total SNPs in outcome: 9,904,926 SNPs
5- Number of common variants between exposure and outcome: 27 SNPs
6- Number of SNPs after harmonization (action=2) = 27 SNPs
Checking weakness of the instruments:
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 15.45 21.17 27.50 67.77 40.96 519.36How many SNPs have been eliminated with checking the weakness: 0 SNP
RUN an initial MR:
## id.exposure id.outcome outcome exposure method nsnp
## 1 HC7LDU hk2Grt outcome exposure MR Egger 23
## 2 HC7LDU hk2Grt outcome exposure Weighted median 23
## 3 HC7LDU hk2Grt outcome exposure Inverse variance weighted 23
## 4 HC7LDU hk2Grt outcome exposure Simple mode 23
## 5 HC7LDU hk2Grt outcome exposure Weighted mode 23
## b se pval
## 1 -1.035502e-04 0.0018656098 0.9562610
## 2 -1.034450e-03 0.0014175453 0.4655447
## 3 1.634319e-04 0.0009975402 0.8698611
## 4 -1.826525e-03 0.0024242238 0.4591693
## 5 3.313507e-05 0.0012753330 0.9795063
## id.exposure id.outcome outcome exposure method Q
## 1 HC7LDU hk2Grt outcome exposure MR Egger 22.97279
## 2 HC7LDU hk2Grt outcome exposure Inverse variance weighted 23.00476
## Q_df Q_pval
## 1 21 0.3454308
## 2 22 0.4014611## id.exposure id.outcome outcome exposure egger_intercept se pval
## 1 HC7LDU hk2Grt outcome exposure 1.078169e-05 6.30744e-05 0.8659103
Testing Outlier with PRESSO test
## $`Main MR results`
## Exposure MR Analysis Causal Estimate Sd T-stat
## 1 beta.exposure Raw 0.0001634319 0.0009975402 0.163835
## 2 beta.exposure Outlier-corrected NA NA NA
## P-value
## 1 0.8713569
## 2 NA
##
## $`MR-PRESSO results`
## $`MR-PRESSO results`$`Global Test`
## $`MR-PRESSO results`$`Global Test`$RSSobs
## [1] 25.02173
##
## $`MR-PRESSO results`$`Global Test`$Pvalue
## [1] 0.447Radial test
##
## Radial IVW
##
## Estimate Std.Error t value Pr(>|t|)
## Effect (Mod.2nd) 0.0001634276 0.0009975406 0.1638306 0.8698645
## Iterative 0.0001634276 0.0009975406 0.1638306 0.8698645
## Exact (FE) 0.0001657918 0.0009755219 0.1699519 0.8650480
## Exact (RE) 0.0001654286 0.0009346680 0.1769918 0.8611342
##
##
## Residual standard error: 1.023 on 22 degrees of freedom
##
## F-statistic: 0.03 on 1 and 22 DF, p-value: 0.871
## Q-Statistic for heterogeneity: 23.00436 on 22 DF , p-value: 0.4014837
##
## No significant outliers
## Number of iterations = 2## [1] "No significant outliers"Studentized residuals:
Cook’s distance
In statistics, Cook’s distance or Cook’s D is a commonly used estimate of the influence of a data point when performing a least-squares regression analysis.[1] In a practical ordinary least squares analysis, Cook’s distance can be used in several ways:
1- To indicate influential data points that are particularly worth checking for validity.
2- To indicate regions of the design space where it would be good to be able to obtain more data points. It is named after the American statistician R. Dennis Cook, who introduced the concept in 1977(Refernce).
Potential Outliers and Influential SNPs
## 11 15
## 0.8849746 0.2038728## [1] 11report After Deleting Influential SNPs:
## id.exposure id.outcome outcome exposure method nsnp
## 1 HC7LDU hk2Grt outcome exposure MR Egger 22
## 2 HC7LDU hk2Grt outcome exposure Weighted median 22
## 3 HC7LDU hk2Grt outcome exposure Inverse variance weighted 22
## 4 HC7LDU hk2Grt outcome exposure Simple mode 22
## 5 HC7LDU hk2Grt outcome exposure Weighted mode 22
## b se pval
## 1 -1.275713e-04 0.0018264414 0.9450092
## 2 -1.042590e-03 0.0013420010 0.4372223
## 3 -1.458760e-05 0.0009834775 0.9881657
## 4 -1.731827e-03 0.0022996324 0.4597566
## 5 1.248827e-05 0.0013174349 0.9925263
## id.exposure id.outcome outcome exposure method Q
## 1 HC7LDU hk2Grt outcome exposure MR Egger 20.96791
## 2 HC7LDU hk2Grt outcome exposure Inverse variance weighted 20.97367
## Q_df Q_pval
## 1 20 0.3990238
## 2 21 0.4605532## id.exposure id.outcome outcome exposure egger_intercept se
## 1 HC7LDU hk2Grt outcome exposure 4.590454e-06 6.190946e-05
## pval
## 1 0.9416293
OR report:
## id.exposure id.outcome outcome exposure method nsnp
## 1 HC7LDU hk2Grt outcome exposure MR Egger 22
## 2 HC7LDU hk2Grt outcome exposure Weighted median 22
## 3 HC7LDU hk2Grt outcome exposure Inverse variance weighted 22
## 4 HC7LDU hk2Grt outcome exposure Simple mode 22
## 5 HC7LDU hk2Grt outcome exposure Weighted mode 22
## b se pval lo_ci up_ci or
## 1 -1.275713e-04 0.0018264414 0.9450092 -0.003707397 0.003452254 0.9998724
## 2 -1.042590e-03 0.0013420010 0.4372223 -0.003672912 0.001587732 0.9989580
## 3 -1.458760e-05 0.0009834775 0.9881657 -0.001942203 0.001913028 0.9999854
## 4 -1.731827e-03 0.0022996324 0.4597566 -0.006239107 0.002775452 0.9982697
## 5 1.248827e-05 0.0013174349 0.9925263 -0.002569684 0.002594661 1.0000125
## or_lci95 or_uci95
## 1 0.9962995 1.003458
## 2 0.9963338 1.001589
## 3 0.9980597 1.001915
## 4 0.9937803 1.002779
## 5 0.9974336 1.002598MendelianRandomization Package
##
## Inverse-variance weighted method
## (variants uncorrelated, random-effect model)
##
## Number of Variants : 22
##
## ------------------------------------------------------------------
## Method Estimate Std Error 95% CI p-value
## IVW 0.000 0.001 -0.002, 0.002 0.988
## ------------------------------------------------------------------
## Residual standard error = 0.999
## Residual standard error is set to 1 in calculation of confidence interval when its estimate is less than 1.
## Heterogeneity test statistic (Cochran's Q) = 20.9737 on 21 degrees of freedom, (p-value = 0.4606). I^2 = 0.0%.
## F statistic = 69.7.## Method Estimate Std Error 95% CI P-value
## Simple median -0.001 0.002 -0.004 0.002 0.510
## Weighted median -0.001 0.001 -0.004 0.002 0.442
## Penalized weighted median -0.001 0.001 -0.004 0.002 0.442
##
## IVW 0.000 0.001 -0.002 0.002 0.988
## Penalized IVW 0.000 0.001 -0.002 0.002 0.988
## Robust IVW 0.000 0.001 -0.002 0.002 0.974
## Penalized robust IVW 0.000 0.001 -0.002 0.002 0.974
##
## MR-Egger 0.000 0.002 -0.004 0.003 0.944
## (intercept) 0.000 0.000 0.000 0.000 0.941
## Penalized MR-Egger 0.000 0.002 -0.004 0.003 0.944
## (intercept) 0.000 0.000 0.000 0.000 0.941
## Robust MR-Egger 0.000 0.002 -0.003 0.003 0.983
## (intercept) 0.000 0.000 0.000 0.000 0.996
## Penalized robust MR-Egger 0.000 0.002 -0.003 0.003 0.983
## (intercept) 0.000 0.000 0.000 0.000 0.996
| id.exposure | id.outcome | exposure | outcome | snp_r2.exposure | snp_r2.outcome | correct_causal_direction | steiger_pval |
|---|---|---|---|---|---|---|---|
| HC7LDU | hk2Grt | exposure | outcome | 0.0468254 | 5.61e-05 | TRUE | 0 |
## $r2_exp
## [1] 0
##
## $r2_out
## [1] 0.25
##
## $r2_exp_adj
## [1] 0
##
## $r2_out_adj
## [1] 0.25
##
## $correct_causal_direction
## [1] FALSE
##
## $steiger_test
## [1] 0
##
## $correct_causal_direction_adj
## [1] FALSE
##
## $steiger_test_adj
## [1] 0
##
## $vz
## [1] NaN
##
## $vz0
## [1] 0
##
## $vz1
## [1] NaN
##
## $sensitivity_ratio
## [1] NaN
##
## $sensitivity_plot
MRraps package
## $beta.hat
## [1] -1.478242e-05
##
## $beta.se
## [1] 0.000998601
##
## $beta.p.value
## [1] 0.9881892
##
## $naive.se
## [1] 0.0009913349
##
## $chi.sq.test
## [1] 20.97367## over.dispersion loss.function beta.hat beta.se
## 1 FALSE l2 -1.478242e-05 0.000998601
## 2 FALSE huber -2.661156e-06 0.001024542
## 3 FALSE tukey -3.333910e-05 0.001024545
## 4 TRUE l2 -9.726443e-05 0.001131137
## 5 TRUE huber -6.804823e-06 0.001024542
## 6 TRUE tukey -3.402461e-05 0.001024545##
## MR-Lasso method
##
## Number of variants : 22
## Number of valid instruments : 22
## Tuning parameter : 0.5001954
## ------------------------------------------------------------------
## Exposure Estimate Std Error 95% CI p-value
## exposure 0.000 0.001 -0.002, 0.002 0.988
## ------------------------------------------------------------------##
## Constrained maximum likelihood method (MRcML)
## Number of Variants: 22
## Results for: cML-MA-BIC
## ------------------------------------------------------------------
## Method Estimate SE Pvalue 95% CI
## cML-MA-BIC 0.000 0.001 0.999 [-0.002,0.002]
## ------------------------------------------------------------------##
## Debiased inverse-variance weighted method
## (Over.dispersion:TRUE)
##
## Number of Variants : 22
## ------------------------------------------------------------------
## Method Estimate Std Error 95% CI p-value Condition
## dIVW 0.000 0.001 -0.002, 0.002 0.988 322.452
## ------------------------------------------------------------------##
## Mode-based method of Hartwig et al
## (weighted, delta standard errors [not assuming NOME], bandwidth factor = 1)
##
## Number of Variants : 22
## ------------------------------------------------------------------
## Method Estimate Std Error 95% CI p-value
## MBE 0.000 0.001 -0.002, 0.002 0.991
## ------------------------------------------------------------------
